Question

CAR WASH To raise money for their rowing club, Halima, Aisha, and Fatima

are advertising a car wash at three different street corners in a neighborhood.
On a map, the coordinates for the corners are (3, 15), (6,4), and (11, 9). Each unit
represents 0.5 kilometer. What is the area of the neighborhood in which they are
advertising?

Answer 1

The area of the neighborhood in which they are advertising is 8.75 km²

Explanation:

The coordinates of the street corners are;

(3, 15), (6, 4) and (11,9)

Therefore;

The distance between each street corner are found using the following formula;

`Distance, \ d=\sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

Substituting, using an online tool, we find the distances;

Between (3, 15) and (6, 4), d = √32.5 km

Between (6, 4) and (11,9), d = √12.5 km

Between (3, 15) and (11,9), d = 5 km

The area is given by Heron's formula as follows;

`A = √(s\cdot \left (s-a \right )\cdot \left (s-b \right ) \cdot \left ( s-c \right ))`

Where;

s = (√32.5 + √12.5 + 5)/2

a = √32.5

b = √12.5

c = 5

Substituting (using an online tool) the values gives;

A = 8.75 km²

The area of the neighborhood in which they are advertising is 8.75 km²