Question

Determine the missing vertex of a right triangle with vertices (6,2) and (5,5) if the third vertex is on the y-axis.

Verify your answer by graphing.

Answer 1

Either a can be 0 or 10/3

Explanation:

Given that a right triangle has vertices as (6,2) and we have to find the third vertex on the y axis

Since the third vertex lie on y axis, it would have coordinates as (0,a)

Using slope formula we can say one pair of sides will be perpendicular

Let A (6,2) B (5,5) and C (0,a)

Slope of AB = change in y coordinate /change in x coordinate = -3

Slope of BC =
`(a-5)/(-5)`

Slope of CA =
`(a-2)/(-6)`

If AB and BC are perpendicular then

`(a-5)/(-5)*-3 = -1\\\\3a-15 = -5\\a=10/3`... i

OR if BC and CA are perpendicular then,

(a-5)(a-2)= -30

`a^2-7a+40 =0\\`

No real roots

OR if CA and AB are perpendicular

(a-2) =-2

a=0

Either a can be 0 or 10/3