Answer:
1.6 units
Step-by-step explanation:
A(-1, 1)
B(3,2)
C(-1, -1)
BC slope: (2 - (-1))/(3 - (-1)) = 3/4
Equation of a line that pass through A(-1, 1) with slope -4/3 (so that it is perpendicular to segment BC)
y - y1 = m(x - x1)
y - 1 = -4/3(x + 1)
Equation of the line that passes through segment BC:
y - y1 = m(x - x1)
y - 2 = 3/4(x - 3)
These two lines intersect is found solving the next system of equations:
y - 1 = -4/3(x + 1) (eq. 1)
y - 2 = 3/4(x - 3) (eq. 2)
Subtractin eq. 2 to eq. 1, we get :
-1 + 2 = -4/3(x + 1) - 3/4(x - 3)
1 = -4/3x - 4/3 - 3/4x + 9/4
1 + 4/3 - 9/4 = -25/12x
1/12*(-12/25) = x
-0.04 = x
Replacing into eq. 1:
y - 1 = -4/3(-0.04 + 1)
y = -1.28 + 1
y = -0.28
The height of the triangle is the distance between A(-1, 1) and (-0.04, -0.28)
d = √[(-1 - (-0.04))² + (1 - (-0.28))²] = 1.6 units
