Question

Which one of the triangles shown is the image of the other triangle after dilation?What are the coordinates of the center of dilation? What is the scale factor? Explain.

Answer 1

Answer:

a) ΔF'G'H' is the image of ΔFGH

b)Center of dilation  (7,-1)

c) Scale factor: $\frac{1}{2}$

Step-by-step explanation:

Question a

Since the smaller triangle is named F'G'H', it means that, it is the image of triangle FGH.

Question B.

To find the center of dilation, draw straight lines through any two corresponding points.

The straight lines will meet at (7,-1).

This is called the center of dilation.

See graph in attachment.

Question c

The scale factor of the dilation is given by;

$k=\frac{|F'G'|}{|FG|}$

$k=\frac{\sqrt{(4-5)^2+(1-5)^2}}{\sqrt{(3-1)^2+(3-11)^2}}$

$k=\frac{\sqrt{1+16}}{\sqrt{4+64}}$

$k=\frac{\sqrt{17}}{\sqrt{68}}$

$k=\frac{\sqrt{17}}{2\sqrt{17}}$

$k=\frac{1}{2}$