Question

rectangle abcd is graphed on the coordinate plane. what is the length of the image of (overline{bd}) after a dilation of scale factor 0.4 centered at the origin? enter a number like 7 in the box.

Explanation:

Step1: Find length of BD before dilation

Use distance - formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $B(- 2,1)$ and $D(-2,-4)$, $x_1=x_2 = - 2$, $y_1 = 1$, $y_2=-4$. Then $BD=\sqrt{(-2+2)^2+(-4 - 1)^2}=\sqrt{0+( - 5)^2}=5$.

Step2: Calculate length after dilation

Multiply the original length by the scale factor. Let the original length be $l_1 = 5$ and scale factor $k = 0.4$. Then the new length $l_2=k\times l_1=0.4\times5 = 2$.

Answer:

2