Question

first, find the length $ell$ of the rectangle by using the distance formula. let the length be equal to $ad$.
$ell=sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
$=sqrt{1-(-4)^2+(7 - 2)^2}$
$=sqrt{__+__}$
$=__$
distance formula
let $(x_1,y_1)=a(-4,2)$ and $(x_2,y_2)=d(1,7)$.
subtract.
simplify.

Explanation:

Step1: Substitute coordinates

Substitute $x_1=-4,y_1 = 2,x_2=1,y_2 = 7$ into the distance formula $l=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
$l=\sqrt{[1-(-4)]^2+(7 - 2)^2}=\sqrt{(1 + 4)^2+5^2}=\sqrt{5^2+5^2}$

Step2: Calculate squares

Calculate the squares of the numbers inside the square - root.
$l=\sqrt{25 + 25}$

Step3: Simplify

Simplify the expression inside the square - root and then the square - root.
$l=\sqrt{50}=5\sqrt{2}$

Answer:

$5\sqrt{2}$