Find the orthocenter for the triangle described by each set of vertices. K (3.-3), L (2,1), M (4,-3)
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(2, - 3.5)

Step-by-step explanation:

K(3, - 3)

L(2, 1)

= = - 4

Slope of perpendicular line is

y - 1 = - 4(x - 2) ⇔ y = - 4x + 9

Equation of the perpendicular to KL from point M(4, - 3) is

y - (- 3) = (x - 4) ⇔ y = x - 4 ....... (1)

L(2, 1)

M(4, - 3)

= = - 2

Slope of perpendicular line is  

y - 1 = - 2(x - 2) ⇔ y = - 2x + 5

Equation of the perpendicular to LM from point K(3, - 3) is

y + 3 = (x - 3) ⇔ y = x - 4.5 ....... (2)

The coordinates of the intersect of lines (1) and (2)

x - 4.5 = x - 4 ⇒ x = 0.5 ⇒ x = 2

y = (2) - 4.5 ⇒ y = - 3.5

(2, - 3.5)

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answer: 1, 3 and 5 are correct

step-by-step explanation: