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The coordinates for the endpoints of Segment AB are A (1, 3) and B (5, 0). Segment AB is dilated by a scale factor of 3 with the origin as the center of dilation to create Segment A′ B′ . Which of the following will be the slope of Segment A′ B′ ?

4/3

Slope of Segment A'B' cannot be determined from the information provided.

-3/4

3/4

Respuesta :

Since A'B' is the dilation of line AB by a factor of 3 with center of dilation as origin O, [tex]\frac{OB'}{OB}[/tex] = [tex]\frac{OA'}{OA}  = 3[/tex] , Where A' stays on extended line of OA and B' stays on extended line of OB.

But always A'B' and AB will be parallel which means

Slope of A'B' = slope of AB = [tex]\frac{3-0}{5-1} = \frac{-3}{4}[/tex]

Hence slope of A'B' = -3/4

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