Question

The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .

Answer 1

m=6,a'b'=3.5 square root 37

Answer 2

Answer:

The slope is m=6 and length of line is $d' =3.5\sqrt{37}$

Step-by-step explanation:

Given : The endpoints of line AB are A(2, 2) and B(3, 8). Line AB is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image line A'B' .

To find : What are the slope (m) and length of line AB?

Solution :

The slope of a line does not change.

Slope formula is,

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope of AB A(2, 2) and B(3, 8) is :  

$m=\frac{8-2}{3-2}\\\\m=\frac{6}{1}\\\\m=6$

Distance formula, $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

The length of AB by distance formula,

$d = \sqrt{(3 - 2)^2+(8-2)^2}\\d = \sqrt{(1)^2+(6)^2}\\d=\sqrt{1+36}\\d=\sqrt{37}$

Line AB is dilated by a scale factor of 3.5.     

The length of A'B' is :

$d' =3.5\times\sqrt{37}\\d' =3.5\sqrt{37}$

Therefore, The slope is m=6 and length of line is $d' =3.5\sqrt{37}$