Question

1. rectangle abcd has consecutive vertices a(-4, -6), b(-4, -1), c(3, -1), and d(3, -6). find the perimeter and area of rectangle abcd. (example 3)

Explanation:

Step1: Calculate length of AB

Since A(-4, -6) and B(-4, -1) share the same x-coordinate, subtract y-values:
$AB = |-1 - (-6)| = |5| = 5$

Step2: Calculate length of BC

Since B(-4, -1) and C(3, -1) share the same y-coordinate, subtract x-values:
$BC = |3 - (-4)| = |7| = 7$

Step3: Calculate perimeter of rectangle

Use perimeter formula $P=2(l+w)$:
$P = 2(5 + 7) = 2\times12 = 24$

Step4: Calculate area of rectangle

Use area formula $A=l\times w$:
$A = 5\times7 = 35$

Answer:

Perimeter: 24
Area: 35