Question

A triangle has vertices at F(-10,6)E(12,6),andD(2,-8). it is dilated by a scale factor of 1/2 with the origin as the center of dilation to form a similar triangle. What are the coordinates of the vertices of the image?

Answer 1

F' (-5, 3)

E' (6, 3)

D' (1, -4)

Step-by-step explanation

We are given the cordinates of the triangle as:

F(-10, 6), E(12, 6) and D(2, -8)

The dilation factor is 1/2.

To find the new cordinates, we simply multiply the cordinates of the triangle given by 1/2.

That is:

`\begin{gathered} F^(\prime)\text{ = }(1)/(2)(-10,\text{ 6) = (}(1)/(2)\cdot\text{ -10, }(1)/(2)\cdot\text{ 6)} \\ F^(\prime)\text{ = (-5, 3)} \\ E^(\prime)\text{ = }(1)/(2)(12,\text{ 6) = (}(1)/(2)\cdot\text{ 12, }(1)/(2)\cdot\text{ 6)} \\ E^(\prime)\text{ = (6, 3)} \\ D^(\prime)\text{ = }(1)/(2)(2,\text{ -8) = (}(1)/(2)\cdot\text{ 2, }(1)/(2)\cdot\text{ -8)} \\ D^(\prime)\text{ = (1, -4)} \end{gathered}`

So, the cordinates of the image are:

F' (-5, 3)

E' (6, 3)

D' (1, -4)