Question

What is the orthocenter of (-4,6) (2,6) (-4,-2)?

 

Answer 1

Given coordinates are: A(−4, −6), B(2,6) and C(−4, −2)

Write the slope formula

 m = (y2−y1)/(x2−x1)

Slope of BC =[(−2)−(6)]/[−4−2] = −8/−6=4/3

Perpendicular Slope of BC = −1/(4/3)= −3/4

Slope of AC = [(2) − (−6)]/[−4−(−4)] = 8/0

Perpendicular Slope of AC = 0

Equation of AD, slope(m) = −3/4 and point A = (−4, −6)

y − y1 = m(x − x1)

y − (−6) = (−3/4)(x− (−4))

4y + 24 = −3x − 12

3x + 4y = −36 ---------------- (1)

Equation of BE, slope(m) = 0 and point B = (2, 6)

y − 6 = 0(x−2)

y=6

Substitute 6 for y in equation (1).

3x + 4y = −36

3x + 4(6) = −36

3x = −60

x=−20

The solution is (x, y) = (−20,6)