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.

Either a can be 0 or 10/3

Step-by-step 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 =

Slope of CA =

If AB and BC are perpendicular then

... i

OR if BC and CA are perpendicular then,

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

No real roots

OR if CA and AB are perpendicular

(a-2) =-2

a=0

Either a can be 0 or 10/3

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5

im not sure

step-by-step explanation: