Question

in quadrilateral abcd, ∠abc is a right angle and ab = 4 units. quadrilateral abcd is dilated by a scale factor of 2 with point b as the center of dilation, resulting in the image quadrilateral abcd. which statement is true? a. ab is 8 units long and lies on the same line as ab. b. ab is 8 units long and lies on a different line than ab. c. ab is 8 units long but lies on a different line than ab. d. ab is 6 units long but lies on a different line than ab.

Explanation:

Step1: Calculate the length of \(AB'\)

Given that \(AB = 4\) units and the scale - factor of dilation is \(k = 2\). When a point or a line - segment is dilated with a scale factor \(k\) and the center of dilation on one of the endpoints of the line - segment, the length of the dilated line - segment \(AB'\) can be calculated using the formula \(AB'=k\times AB\). Substituting \(k = 2\) and \(AB = 4\) into the formula, we get \(AB'=2\times4 = 8\) units. And the points \(A\), \(B\), and \(B'\) are collinear (lie on the same line) since the center of dilation is \(B\).

Answer:

C. \(AB'\) is 8 units long and lies on the same line as \(AB\).