The distance from the coffee shop to the
school is 10 miles. On
the map, the coffee
shop is 7.5 inches from
the school. Which one
of the following gives
the scale used
on the map?

A. 5 inches = 2 miles
B. 4 inches = 3 miles
C. 2 inches = 5 miles
D. 3 inches = 4 miles

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²