Transformations and vectors

Triangle A is reflected in the x-axis to give triangle B. Write down the coordinates of the vertices of triangle B.

Triangle A is translated by the vector \(\begin{pmatrix}-4\\2\end{pmatrix}\) to give triangle C. Write down the coordinates of the vertices of triangle C.

P is rotated 90° clockwise about the origin. Write down the coordinates of its image.

P is rotated 180° about the origin. Write down the coordinates of its image.

P is reflected in the line y = x. Write down the coordinates of its image.

Describe fully the single transformation that maps triangle A onto triangle B.

Describe fully the single transformation that maps triangle A onto triangle C.

Write down the coordinates of the vertices of triangle U.

Find the area of triangle U.

Describe fully the single transformation that maps triangle A onto triangle B.

Triangle A is reflected in the line y = −x. Write down the coordinates of the vertices of the image.

Triangle ABC is reflected in the y-axis. Write down the coordinates of the images of A, B and C.

Triangle ABC is translated by the vector \(\begin{pmatrix}-3\\2\end{pmatrix}\). Write down the coordinates of the images of A, B and C.

Triangle PQR is mapped onto triangle P′Q′R′ with P′ = (−2, 1), Q′ = (−5, 1) and R′ = (−5, 3). Describe fully the single transformation that maps PQR onto P′Q′R′.

Triangle PQR is mapped onto triangle P″Q″R″ with P″ = (2, −4), Q″ = (5, −4) and R″ = (5, −2). Describe fully the single transformation that maps PQR onto P″Q″R″.

Write down the coordinates of the vertices of the image.

Work out the perimeter of the image, in cm.

The robot's position A is rotated through 90° clockwise about O. Write down the coordinates of its new position.

A second position B = (−2, 4) is rotated through 180° about O. Write down the coordinates of its new position.

A third position C = (5, −2) is rotated through 90° anticlockwise about O. Write down the coordinates of its new position.

The hive is moved by the translation \(\begin{pmatrix}5\\-4\end{pmatrix}\) to point P. Write down the coordinates of P.

The hive is then moved from P to Q(−1, 2). Write down the column vector of the translation that moves the hive from P to Q.

Find the column vector of the single translation that moves the hive from H directly to Q.

T is reflected in the line x = 6. Write down the coordinates of the vertices of the image.

Describe fully the single transformation that maps T onto the triangle with vertices (2, −1), (2, −3) and (5, −1).

Write down a + b as a column vector.

Work out 3a − 2b.

Write down the column vector of the displacement that returns the trolley to its start after a + b.

Write down the column vector \(\overrightarrow{AB}\).

The point C is such that \(\overrightarrow{AC}=2\overrightarrow{AB}\). Find the coordinates of C.

Write down the column vector \(\overrightarrow{CA}\).

Write down the column vector of this translation.

The sprite makes the same move again from T. Write down its new coordinates.

Write down the column vector of the translation that takes the sprite from (−2, 12) straight back to S.

The triangle is reflected in the line x = −1. Write down the coordinates of the image of each vertex.

Describe fully the single transformation that maps the original triangle onto the triangle with vertices (1, −2), (4, −2) and (4, −5).

90° clockwise

180°

90° anticlockwise

Write down the coordinates of the images P′, Q′ and R′.

Describe fully the single transformation that maps P′Q′R′ back onto PQR.

Triangle ABC is reflected in the line x = 5. Write down the coordinates of the images of A, B and C.

Triangle ABC is reflected in the x-axis. Write down the coordinates of the image of C.

Point B(4, 2) is reflected in a horizontal mirror line and its image is (4, 8). Find the equation of the mirror line.

S is rotated through 90° clockwise about the origin. Write down the coordinates of its image.

S is rotated through 180° about the point (1, 1). Find the coordinates of its image.

T is rotated through 90° anticlockwise about the origin. Write down the coordinates of its image.

Write down the coordinates of the corners of the image.

Work out the area of the image.

Triangle PQR is reflected in the y-axis. Write down the coordinates of the images of P and R.

Describe fully the single transformation that maps triangle PQR onto the triangle with vertices (2, −1), (5, −1) and (5, −4).

Calculate the area of the survey region PQR.

Write the translation as a column vector.

The same translation is applied to the point B(−3, 4). Find the coordinates of the image of B.

The same translation moves a point C to C′(9, −5). Find the coordinates of C.

Write down the scale factor of the enlargement.

The point B(3, 5) is mapped to B′ by the same enlargement. Find the coordinates of B′.

The point C is mapped to C′(10, −6) by the same enlargement. Find the coordinates of C.

Write down the coordinates of A′, B′ and C′.

Describe fully the single transformation that maps triangle A′B′C′ onto triangle ABC.

Write down the coordinates of B.

Write down the coordinates of C.

Write the single translation that takes the character directly from A to C as a column vector.

Write down the coordinates of the vertices of Q.

Triangle R has vertices (1, −1), (3, −1) and (3, −4). Describe fully the single transformation that maps P onto R.

Write down the coordinates of A′, B′ and C′.

Describe fully the single transformation that maps A′B′C′ onto ABC.

Write the single translation that maps T onto V as a column vector.

Vertex A(1, 6) of T maps to a vertex of V. Write down the coordinates of that vertex.

Describe fully the single transformation that maps V onto T.

Write down the coordinates of the new position of the marker.

A second marker at P(7, 1) is moved to Q(3, −4) by a single translation. Write down the column vector of this translation.

T is reflected in the line x = 6. Write down the coordinates of the vertices of the image.

Describe fully the single transformation that maps T onto the triangle with vertices (2, −1), (5, −1) and (2, −4).

The point P(3, 1) is rotated through 90° clockwise about the origin O. Write down the coordinates of the image of P.

The point Q(−2, 4) is rotated through 180° about O. Write down the coordinates of the image of Q.

A single rotation about O maps R(4, 0) onto R′(0, 4) and S(0, 2) onto S′(−2, 0). Describe fully this rotation.

Write down the column vector \(\overrightarrow{AB}\).

Write down the column vector \(\overrightarrow{BC}\).

Find the column vector \(\overrightarrow{AC}\).

Write down the coordinates of B.

The scout is then moved from B to C(3, −1) by a single translation. Write down the column vector of this translation.

Write down the column vector of the translation that moves the scout from C back to A.

Write down the coordinates of the image of A in triangle U.

Triangle V has vertices (−1, −2), (−4, −2) and (−4, −5). Describe fully the single transformation that maps T onto V.

Write down the column vector that moves the particle from P to Q.

Calculate the distance PQ.

Calculate the distance PR. Give your answer correct to 3 significant figures.

Write down the coordinates of the image of the vertex (3, 2).

Work out the area of the image rectangle.

The original sprite is instead enlarged by scale factor 2 with centre (1, 1). Find the coordinates of the image of the vertex (3, 2).

Write down the coordinates of U.

The turtle then swims from U to V(6, 1). Write down the column vector of the translation that maps U to V.

Describe fully the single transformation that maps T to V.

P is reflected in the line y = 3. Write down the coordinates of the image of P.

Q is reflected in the line x = −1. Find the coordinates of the image of Q.

A triangular roof panel with vertices (1, 2), (1, 5) and (3, 2) is mapped onto the panel with vertices (−1, 2), (−1, 5) and (−3, 2). Describe fully the single transformation.

Write down the lengths of the sides of rectangle B.

Calculate the perimeter of rectangle B.

Rectangle C is also an enlargement of rectangle A and has a perimeter of 88 cm. Find the scale factor of this enlargement.

Describe fully the single transformation that maps ABC onto A′B′C′.

The same transformation maps the point (10, −7) onto a point R. Find the coordinates of R.

The same transformation maps point D onto D′(5, 2). Find the coordinates of D.

Q is reflected in the line x = 2 to give quadrilateral R. Write down the coordinates of the vertices of R.

R is reflected in the line y = −1 to give quadrilateral S. Write down the coordinates of the vertices of S.

Describe fully the single transformation that maps Q onto S.

Triangle T is rotated 90° anticlockwise about the point (1, 0) to give triangle V. Find the coordinates of the vertices of triangle V.

Describe fully the single transformation that maps triangle V back onto triangle T.

Describe fully the single transformation that maps triangle P onto triangle Q.

Find the area of triangle Q.

Write down the vector of the single translation that has the same effect as these two translations.

After both translations, one vertex of the shape is at (1, 7). Find the coordinates of this vertex before the translations.

Write down the vector of the translation that maps the final shape back onto the original shape.

(Extended) Find the distance moved by each point under the single translation that has the same effect as both translations. Give your answer to 3 significant figures.

T is rotated 90° clockwise about the origin to give triangle U. Write down the coordinates of the vertices of U.

U is reflected in the x-axis to give triangle V. Write down the coordinates of the vertices of V.

Describe fully the single transformation that maps triangle T onto triangle V.

Triangle T is mapped onto triangle U with vertices (−1, −1), (−3, −1) and (−3, −4). Describe fully the single transformation that maps T onto U.

Triangle T is reflected in the line x = 4. Write down the coordinates of the vertices of the image.

Triangle T is mapped onto triangle V with vertices (1, −1), (3, −1) and (3, −4). Describe fully the single transformation that maps T onto V.

Find the coordinates of A′, B′ and C′.

Describe fully the single transformation that maps triangle A′B′C′ onto triangle ABC.

The marker is translated by the vector \(\begin{pmatrix}4\\2\end{pmatrix}\). Write down the coordinates of its three vertices after the translation.

This image is then rotated through 90° clockwise about the origin. Write down the coordinates of its three vertices after the rotation.

State whether the final triangle is congruent to the original triangle, or only similar. Give a reason.

The garden is rotated through 90° clockwise about the origin O. Write down the coordinates of the images A′, B′ and C′.

The triangle A′B′C′ is mapped onto the triangle with vertices (−1, 1), (−1, 4) and (−3, 4). Describe fully the single transformation.

Write down the coordinates of the vertices of the image.

Calculate the perimeter of the image, in cm.

Describe fully the enlargement that maps P onto Q.

Q is translated by \(\begin{pmatrix}-5\\-2\end{pmatrix}\). Write down the image of the point (7, 5) under this translation.

P is transformed by X, and then its image is transformed by Y. Find the final coordinates.

P is transformed by Y, and then its image is transformed by X. Find the final coordinates.

Does the order of the two transformations matter? Give a reason.

Write down the coordinates of the image of each vertex.

Describe fully the single transformation that maps A′B′C′ back onto ABC.

Find the coordinates of the vertices of the image.

Write down the length, in cm, of the image of the side from (2, 1) to (2, 3).

Describe fully the single transformation that maps A onto B.

A is rotated 90° anticlockwise about the origin, and the image is rotated 90° anticlockwise about the origin again. Describe fully the single transformation that maps A onto the final image.

Write down \(\overrightarrow{AC}\) as a column vector.

Work out \(2\overrightarrow{AB}-\overrightarrow{BC}\).

Find the coordinates of C.

T is reflected in the line y = 2. Write down the vertices of the image.

The image from (a) is enlarged by scale factor 2 with centre the origin. Write down the vertices of the new image.

Describe fully the enlargement that maps X onto Y.

Find the image of the point (3, 4) under the same enlargement.

Find the coordinates of A′, B′ and C′.

Work out the area of triangle A′B′C′.

The triangle is reflected in the line y = x. Write down the coordinates of the three corners of the image.

Another image of PQR has corners (−4, −1), (−1, −1) and (−1, −3). Describe fully the single transformation.

A point is reflected in the line y = x and its image is (7, −2). Write down the coordinates of the original point.

Describe fully the single transformation that maps M onto N.

Work out the area of triangle N.

Q is reflected in the line \(y=x\). Write down the coordinates of the four images.

Describe fully the single transformation that maps Q onto the quadrilateral with vertices (−2, −1), (−5, −1), (−5, −3) and (−3, −3).

Describe fully this enlargement.

The same enlargement maps the point P(5, 4) onto P′. Find the coordinates of P′.

Calculate the area of triangle A′B′C′.

Describe fully this rotation.

Triangle ABC is also rotated through 180° about the point (2, 2). Find the coordinates of the image of B.

Write down the coordinates of A′, B′ and C′.

Write down the coordinates of A″, B″ and C″.

Describe fully the single transformation that maps triangle ABC onto triangle A″B″C″.