Question

A is the point (0,8) and B is the point (8,6). Find the point C on the y-axis such that angle ABC is 90 degrees. Please show you work.

Answer 1

C = (0,8)

Step-by-step explanation:

If

A = (0,8) = (x1, y1) say

Then A lies on y axis

B=(8, 6) = (x2, y2) say

If C lies on y axis then C is of the form (0, a)

Since AB and BC are perpendicular ( since angle ABC =90°)

(Slope of AB) (Slope of BC) =-1

(6-8)/(8-0)=(a-6)/(0-8)

2=a-6

a=8

Answer 2

The required coordinate C (0, -26)

Given:

A is the point (0,8) and B is the point (8,6)

To find:

Find the point C on the y-axis such that angle ABC is 90 degrees

Solution:

Given A (0,8) and B (8,6)

Let (x, y) be point C

Given that C lies on y -axis, then the coordinate of x = 0

Then the required point C(x,y) = (0, y)

Given that the angle ABC = 90°

If we join AB and BC then line AB will be perpendicular to line BC

As we know

The Product of slopes Perpendicular lines AB and BC = -1  

A (0,8) and B (8,6)

Slope of AB = (6 - 8) / (8 -0) =  -2/8 = -1/4  

B (8, 6) and C (0, y)

Slope of BC = (y - 6)/(0-8) = (y - 6)/-8

⇒ Slope of AB × Slope of BC = - 1

⇒ Slope of AB = - ( 1/Slope of BC )

⇒ -1/4 = - [-8 /(y-6) ]

⇒  1(y-6) = (-8)(4)

⇒  y-6 = -32

⇒  y = - 26

The required coordinate C (0, -26)

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