Shape and Space 5

Write down the column vector that translates the point (–2, 5) to the point (1, 3).

Triangle P with vertices A(1, 1), B(4, 1) and C(1, 4) is translated by the vector , then reflected in the line . Give the coordinates of the vertices after both transformations. Show all your working.

The diagram shows trapezium Q with vertices at (2, 1), (6, 1), (6, 3), and (2, 3).

a) Write down the vector that translates Q so that P1 moves to (4, –2).

b) What are the new coordinates of P3 after the translation?

Describe fully the single transformation that maps the triangle with vertices (3, 2), (6, 2), (6, 5) onto the triangle with vertices (–3, 2), (–6, 2), (–6, 5).

How are the object and the image related if a shape is reflected or rotated? Write one word.

A shape is enlarged by a scale factor of 3 about the centre (0, 0). One vertex of the original shape is at (–2, 4). What are the coordinates of the corresponding vertex on the image? Show your working.

A square has been enlarged by scale factor about the origin to produce a new square. The sides of the new square are 12 units long, and the original square's sides are 4 units long. Find the value of .

Fill in the missing vector (column vector form) for each transformation based on the given movement: