Unit 5

Explain why the product of the gradients of two perpendicular lines (neither vertical nor horizontal) is always -1.

The equation of a quadratic curve is . The graph of is transformed to the graph of .

Write down the equation of the transformed graph in terms of .

Calculate the coordinates of the new vertex (minimum point) after these transformations.

Consider the function . The graph of passes through the point (2, 10) and has a stationary point at .

Find the values of and . Show all reasoning.

Write down the equation of the line that is the mirror line for a reflection in the x-axis.

What is the scale factor of an enlargement if a triangle with side length 3 is enlarged to make a triangle with side length 6?

A triangle has vertices at (1, 2), (3, 2) and (1, 4). It is translated by the vector .

A triangle is reflected in the y-axis. The image of the point (–4, 5) is point A. What are the coordinates of point A?

Write the column vector that translates the point (0, –2) to the point (3, 4).

Which transformation always preserves shape and size?

Two rectangles are similar. Rectangle X has sides 4 cm and 7 cm. Rectangle Y has sides 8 cm and k cm. Work out the value of k.