Question

Triangle XYZ where X(7, 2), Y(-3, 8), and Z(-4, 6) is dilated with a scale factor of 2/3 Where is the dilation located?

Answer 1

Solution : Option A

Explanation:

We are given Triangle XYZ, where X(7, 2), Y(-3, 8), and Z(-4, 6) is dilated with a scale factor of 2/3. To determine where the dilation is located, we will have to multiply the coordinates of each point by the given scale factor of 2 / 3. It will be as follows.

X(7, 2) ⇒
`\left(7\:\cdot \:(2)/(3),\:2\cdot (2)/(3)\:\right)` =
`(14 / 3, 4 / 3)`

Y(- 3, 8) ⇒
`\left(-3\:\cdot \:(2)/(3),\:8\cdot (2)/(3)\:\right)` =
`(-2, 16 / 3)`

Z(- 4, 6) ⇒
`\left(-4\:\cdot \:(2)/(3),\:6\cdot (2)/(3)\:\right)` =
`(-8/3,4)`

As you can see your solution is option a. We have our dilated points as X'( 14 / 3, 4 / 3 ), Y'(- 2, 16 / 3), and Z'(- 8 / 3, 4).

Answer 2

For X: 2/3(7,2)= X'(14/3, 4/3)

For Y: 2/3(-3,8)= Y'(-2, 16/3)

For Z: 2/3(-4, 6)= Z'(-8/3, 4)

solution is a