Question

WILL FAN AND MEDAL!! Dilation problem!!!

Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′. If M = (2, 4) and N = (3, 5), what is the slope of line M'N'?

Answer 1

slope=((y2)−(y1))/((x2)−(x1))=(5-4)/(3-2)=1/1=1 The answer is one

Answer 2

Slope of line M'N' is 1.

Explanation:

Given: M= (2,4) and N = (3, 5) ; K = 0.8

The rule of dilation with origin as the center:

`(x ,y) \rightarrow (kx , ky)` where k is the scale factor i.e k = 0.8

or
`(x ,y) \rightarrow (0.8x , 0.8y)`

Then:

Apply this on coordinates of MNOPQ to find M' and N'.

`M(2 ,4) * (0.8\cdot 2 , 0.8\cdot 4)` = M'(1.6 , 3.2)

`N(3 ,5) * (0.8\cdot 3 , 0.8\cdot 5)` = N'(2.4 , 4)

Slope of line for any two points
`(x_1 , y_1)` and
`(x_2, y_2)` is given by:

`m = (y_2-y_1)/(x_2-x_1)`

To find the slope of line M'N':

we have M' = (1.6 , 3.2) and N' = (2.4, 4)

then by slope formula;

Slope of line M'N' =
`(4-3.2)/(2.4-1.6)=(0.8)/(0.8) = 1`

Therefore, slope of line M'N' is 1.