Question

Draw the image of ABC under a dilation whose center is P and scale factor is 2.

Please assist right away! Any unnecessary answers will be reported.

Answer 1

Answer: See the diagram below

Step-by-step explanation:

To go from P to A we follow these two steps (in any order)

• Go right 3 units
• Go up 2 units

After arriving at point A, move another "right 3, up 2" to arrive at point A'.

Then move back to point P. The goal is to travel to point B. Follow these motions in any order:

• Move left 3 units
• Move up 3 units

Repeat this motion to go from B to B'

Move back to point P. Move down 2 units to arrive at point C. Move another 2 units to arrive at point C.

This is all shown in the diagram below. Triangle A'B'C' has been enlarged by a scale factor of 2. It means that the sides of ABC have been doubled to get the corresponding sides of A'B'C'.

In other words,

• A'B' = 2*AB
• B'C' = 2*BC
• A'C' = 2*AC

Also,

• PA' = 2*PA
• PB' = 2*PB
• PC' = 2*PC

These last three equations show that the distance from P to the new points (A',B',C') has been doubled compared to the original three points (A,B,C). Let me know if you have any questions.