A dilation has center at origin. Which of the following is the image of the point p (7/4-5/2) for a scale factor of 1/7

Question

asked Dec 14, 2019 136k views

2 Answers

Pczeus · Answer 1 · 2019-12-20T12:24:39+0000

Answer:

The image of the point p is
p'((1)/(4),(-5)/(14)) .

Explanation:

The center of dilation is origin and the scale factor is
(1)/(7) .

The coordinates of point p are

((7)/(4),(-5)/(2))

If k is the scale factor and origin is the center of dilation, then

$(x,y)\rightarrow (kx,ky)$

Since the scale factor is
(1)/(7) and the origin is the center of dilation, therefore

$(x,y)\rightarrow ((1)/(7)x,(1)/(7)y)$

The coordinates of image of p are

$p((7)/(4),(-5)/(2))\rightarrow p'((1)/(7)* (7)/(4),(1)/(7)* (-5)/(2))$

$p((7)/(4),(-5)/(2))\rightarrow p'((1)/(4),(-5)/(14))$

Therefore the image of the point p is
p'((1)/(4),(-5)/(14)) .