Dilations Practice

Question

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Question
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A coordinate plane with four quadrants shows x-axis ranging from negative 5 to 12 in increments of 1 and the y-axis from 17 to negative 4 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 1. The plotted points are as follows: Upper A is left parenthesis 2 comma 3 right parenthesis and upper B is left parenthesis 4 comma 1 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 6 comma 9 right parenthesis and upper B prime as left parenthesis 12 comma 3 right parenthesis. The points are joined by a line.

Determine the scale factor used in the dilation of line segment AB , centered at the origin.

(1 point)

Answer 1

The scale factor used in the dilation of line segment AB is 2.

Answer 2

no

Answer 3

Apologies for the incorrect response. To determine the scale factor used in the dilation of line segment AB, we can compare the lengths of the original line segment AB and the corresponding line segment A'B' after dilation.

The length of line segment AB can be found using the distance formula:

AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(4 - 2)^2 + (1 - 3)^2]
= √(2^2 + (-2)^2)
= √(4 + 4)
= √8
= 2√2

The length of line segment A'B' can be found using the same formula:

A'B' = √[(x2' - x1')^2 + (y2' - y1')^2]
= √[(12 - 6)^2 + (3 - 9)^2]
= √(6^2 + (-6)^2)
= √(36 + 36)
= √72
= 6√2

Therefore, the scale factor is 6√2 / 2√2 = 6/2 = 3.