A right triangle has the following vertices. Find the area of the triangle. (7,-3), (4,-3), (4,9)
(A.) 18 square units
(B.) 36 square units
(C.) 27.4 square units
(D.) √153 square units

Step-by-step explanation:

Ara of a triangle = 1/2 * base * height.

Before we find the area, we must look for all the sides of the triangle by taking the difference between any two points.

Given D = √(x₂-x₁)²+(y₂-y₁)²

Given the coordinates P(7,-3), Q(4,-3), R(4,9)

For the coordinates P(7,-3), Q(4,-3)

Given PQ = √(4-7)²+(-3+3)²

PQ = √(-3)²+0

PQ =  √9

PQ = 3

For coordinates P(7,-3), R(4,9)

Given PR = √(4-7)²+(9+3)²

PR = √(-3)²+12²

PR =  √9+144

PR = √153

For coordinates Q(4,-3), R(4,9)

Given QR = √(4-4)²+(9+3)²

QR = √(0)²+12²

QR =  √0+144

QR = 12

Since it is a rright angled triangle, the base of the triamgle will be QR and the height will be PQ since the longest side is PR

Area of the triangle = 1/2 * PQ*QR

Area of the triangle = 1/2 * 12*6

Area of the triangle = 6*6

Area of the triangle = 36 square units

after simplifying it i got: -36.25 as my answer. hope that !