Question

Segment cd has endpoints at c(5, 0) and d(11, 0). If the segment is dilated by a factor of one half about point c, what is the length of the image of segment cd?

1) 3
2) 6
3) 12
4) 22

Answer 1

To find the length of the image of segment CD after dilating it by a factor of one half about point C, we calculate the original length (6) and then multiply by ½, resulting in a new length of 3.

Step-by-step explanation:

The question asks about the dilation of segment CD with endpoints C(5, 0) and D(11, 0) by a factor of one half about point C. To find the length of the image of segment CD after the dilation, we first calculate the original length of CD. The coordinates of C and D are both on the x-axis, so we can find the length by subtracting the x-coordinate of C from the x-coordinate of D.

Length of CD = Dx - Cx = 11 - 5
Original length of CD = 6

Since the dilation factor is one half, we multiply the original length by ½ to get the length of the dilated image of CD.

Length of the image of CD = ½ × Original length of CD = ½ × 6 = 3

Therefore, the correct answer is option 1) 3.