Question

If △ABC is dilated by a scale factor of 1/2 with a dilation center of A, what is the coordinates of point C?

Answer 1

To determine the coordinates of point C after dilation by scale factor k=1/2, you have to multiply each coordinate of the original point by the scale factor, following the rule:

`(x,y)\to((1)/(2)x,(1)/(2)y)`

First, determine the coordinates of C. The point is over the x-axis, so the y-coordinate is zero, the x-coordinate can be read from the graph, it is x=2

C(2,0)

Calculate the dilation as follows:

`C(2,0)\to C^(\prime)((1)/(2)\cdot2,(1)/(2)\cdot0)=C^(\prime)(1,0)`

The coordinates of point C after the dilation are C'(1,0)