Under a dilation, the point (2,6) is moved to (6,18) what is the scale factor of the dilation? enter your answer in the box

Question

asked Jun 5, 2020 184k views

2 Answers

ShanePowser · Answer 1 · 2020-06-09T11:50:15+0000

Explanation:

The equation of line passing through the two points is
(y-y_(1) )/(x-x_(1) )=(y_(2) -y_(1))/(x_(2) -x_(1))

When substituted,the equation becomes
(y-6)/(x-2)=(18-6)/(6-2)

which when simplified is
y=3* x

The line clearly passes through origin.

The distance between two points is
$\sqrt{(y_(1)-y_(2) )^(2)+(x_(1)- x_(2) )^(2)}$

Distance between origin and
(2,6) is
√(40) .

Distance between origin and
(6,18) is
√(360)

Scale factor is
$\frac{distance\text{ }of\text{ }p_(2)\text{ from origin}}{distance \text{ } of \text{ } p_(1)\text{ from origin}}$

So,scale factor is
(√(360) )/(√(40) )

which when simplified becomes 3.