Question

Can you please help me

Answer 1

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is
`(3)/(4)` ⇒ B

Explanation:

In similar rectangles, their corresponding dimensions are proportional, which means
`(L_(1) )/(L_(2))` =
`(W_(1) )/(W_(2))` , where L is the length and W is the width

∵ Rectangle ABCD is similar to rectangle MNOP

∴ Their dimensions are proportional

∵ The dimensions of rectangle ABCD are 6 m, 14 m

∴ L
`_(1)` = 14 and W
`_(1)` = 6

∵ The dimensions of rectangle MNOP are 4.5 m, 10.5 m

∴ L
`_(2)` = 10.5 and W
`_(2)` = 4.5

∵ The rectangle MNOP is the image of rectangle ABCD after dilation

→ To find the scale factor of dilation find the ratio between the

corresponding dimensions in the two rectangles (image/pre-image)

∵
`(L_(2) )/(L_(1))` =
`(10.5)/(14)` =
`(3)/(4)`

∵
`(W_(2) )/(W_(1))` =
`(4.5)/(6)` =
`(3)/(4)`

∴ The scale factor for the dilation is
`(3)/(4)`

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is
`(3)/(4)`