Question

Can you please help me

Answer 1

Answer:

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is  $\frac{3}{4}$ ⇒ B

Step-by-step explanation:

In similar rectangles, their corresponding dimensions are proportional, which means $\frac{L_{1} }{L_{2}}$ = $\frac{W_{1} }{W_{2}}$ , 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)

∵ $\frac{L_{2} }{L_{1}}$ = $\frac{10.5}{14}$ = $\frac{3}{4}$

∵ $\frac{W_{2} }{W_{1}}$ = $\frac{4.5}{6}$ = $\frac{3}{4}$

∴ The scale factor for the dilation is  $\frac{3}{4}$

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is  $\frac{3}{4}$