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)

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is