Question

1. a rectangle in the coordinate plane has vertices a(-1, 0) and d(11, -5). find the area if ab is 3.

Explanation:

Step1: Calculate length of AD

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(-1,0)$ and $(x_2,y_2)=(11,-5)$.
$AD=\sqrt{(11 - (-1))^2+(-5 - 0)^2}=\sqrt{(12)^2+(-5)^2}=\sqrt{144 + 25}=\sqrt{169}=13$

Step2: Calculate area of rectangle

Area of rectangle $A = AB\times AD$. Given $AB = 3$ and $AD = 13$.
$A=3\times13 = 39$

Answer:

39