Answer:
(2, - 3.5)
Step-by-step explanation:
K(3, - 3)
L(2, 1)
[tex]m_{KL}[/tex] = [tex]\frac{-3-1}{3-2}[/tex] = - 4
Slope of perpendicular line is [tex]\frac{1}{4}[/tex]
y - 1 = - 4(x - 2) ⇔ y = - 4x + 9
Equation of the perpendicular to KL from point M(4, - 3) is
y - (- 3) = [tex]\frac{1}{4}[/tex] (x - 4) ⇔ y = [tex]\frac{1}{4}[/tex] x - 4 ....... (1)
L(2, 1)
M(4, - 3)
[tex]m_{LM}[/tex] = [tex]\frac{-3-1}{4-2}[/tex] = - 2
Slope of perpendicular line is [tex]\frac{1}{2}[/tex]
y - 1 = - 2(x - 2) ⇔ y = - 2x + 5
Equation of the perpendicular to LM from point K(3, - 3) is
y + 3 = [tex]\frac{1}{2}[/tex] (x - 3) ⇔ y = [tex]\frac{1}{2}[/tex] x - 4.5 ....... (2)
The coordinates of the intersect of lines (1) and (2)
[tex]\frac{1}{2}[/tex] x - 4.5 = [tex]\frac{1}{4}[/tex] x - 4 ⇒ [tex]\frac{1}{4}[/tex] x = 0.5 ⇒ x = 2
y = [tex]\frac{1}{2}[/tex] (2) - 4.5 ⇒ y = - 3.5
(2, - 3.5)
