Question

On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negative 1, negative 1)
If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

0.625 units
0.8 units
1.25 units
1.6 units

Answer 1

Compute the perpendicular distance from A(-1,1) to the line through B(3,2) and C(-1,-1).

Equation of BC: from points B and C,
slope = (2 - (−1))/(3 - (−1)) = 3/4, so 4y = 3x − 1 or 3x − 4y − 1 = 0.

Distance = |3(−1) − 4(1) − 1| / sqrt(3^2 + (−4)^2) = |−8| / 5 = 8/5 = 1.6 units.

Answer: 1.6 units.