Question

What are the vertices of (A4BC).when it is dilated %, graph the transformation?12SBCA'B'CIs this an enlargement or reduction?

Answer 1

A' (-1, 2)

B' (2, 1)

C' (-2, -2)

This dilation represents a reduction.

Step-by-step explanation

A dilation means the size is increased or decreased. If the scale factor is less than 1, then the size is decreased, but if the scale factor is more than 1, it means the figure is enlarged.

Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates

(kx, ky).

So, we need to first write the coordinates of the triangle

A (-2, 4)

B (4, 2)

C (-4, -4)

So dilating by ½, the coordinates become

A (-2, 4) = A' [½(-2), ½(4)] = A' (-1, 2)

B (4, 2) = B' [½(4), ½(2)] = B' (2, 1)

C (-4, -4) = C' [½(-4), ½(-4)] = C' (-2, -2)

The scale factor is ½, which is less than 1, hence, this dilation represents a reduction.

Hope this Helps!!!