Question

in figure the vertices of triangle abc are a(0,6) b(8,0)c(5,8) if cd is perpendicular to ab then find the length of the altitude of cd​

Answer 1

Given info : The vertices of triangle ABC are A (0, 6), B(8, 0) and C(5, 8). CD is perpendicular to AB.

To find : the length of the altitude from C to AB, i.e., CD is ..

solution : slope of AB = (0 - 6)/(8 - 0) = -6/8 = -3/4

as CD is perpendicular to AB.

slope of CD × slope of AB = -1

⇒slope of CD × -3/4 = -1

⇒slope of CD = 4/3

now equation of CD :

(y - 8) = 4/3(x - 5)

⇒3y - 24 = 4x - 20

⇒4x - 3y + 4 = 0...(1)

and equation of AB :

(y - 6) = -3/4(x - 0)

⇒4y + 3x - 24 = 0....(2)

from equations (1) and (2) we get,

x = 56/25 and y = 108/25

now, C(56/25, 108/25) = (2.24, 4.32)

now using distance formula,

Length of altitude CD = √{(5 - 2.24)² + (8 - 4.32)²}

= 4.6 unit

Therefore the length of altitude from C to AB is 4.6 unit .

Answer 2

Step-by-step explanation:

in the given figure the vertices of a triangle abc are a(0,6),b(8,0) and c(5,8).if cd perpendicular ab find the altitude of the triangle abc