Question

Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The coordinates of the vertices of triangle RST are given. You can use the scale factor to find the coordinates of the dilated image. Enter the coordinates of the vertices of triangle R'S'T' below. (Decimal values may be used.)

Answer 1

Triangle RST was dilated by a scale factor of 1/2

Given: triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. 

Pre-image: 

measure of pre-image * scale factor = measure of resulting image

measure of pre-image = measure of resulting image / scale factor

measure of pre-image = 8 / 1/2

measure of pre-image = 8 * 2/1 

measure of pre-image = 16 units.

Step-by-step explanation:

Answer 2

The coordinates of the image of the dilation are $R' = (-3.75,2.25)$, $S' = (2.25,3)$ and $T' = \frac{3}{4} \times (2.25,4.5)$

Dilation

Dilation involves changing the size of a shape

Coordinates

The coordinates of triangle RST are given as

$R = (-5,3)$

$S = (3,4)$

$T = (3,-6)$

The scale factor is given as:

$k = \frac 34$

The rule of dilation using the origin as the center of dilation is:

$(x,y) \to k(x,y)$

So, we have:

$R' = \frac{3}{4} \times (-5,3)$

$R' = (-3.75,2.25)$

$S' = \frac{3}{4} \times (3,4)$

$S' = (2.25,3)$

$T' = \frac{3}{4} \times (3,6)$

$T' = \frac{3}{4} \times (2.25,4.5)$

Hence, the coordinates of the image of the dilation are

$R' = (-3.75,2.25)$, $S' = (2.25,3)$ and $T' = \frac{3}{4} \times (2.25,4.5)$

Read more about dilation at:

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