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.

Answer 1

Answer:

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 = $\frac{a-5}{-5}$

Slope of CA = $\frac{a-2}{-6}$

If AB and BC are perpendicular then

$\frac{a-5}{-5}*-3 = -1\\\\3a-15 = -5\\a=10/3$... 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