Distance between two point `(8, -4)` and `(0, a)` is `10`. All the values are in the same unit of length. Find the positive value of a.

Answer

2

Explanation

Let P(8, -4) and Q(0, a) be two points, distance PQ is 10.
`therefore " "` According to distance formula
PQ = `sqrt((x_2-x_1)^(2) + (y_2-y_1)^(2))`
`" "=sqrt((0-8)^(2) + (a+4)^(2))`
`rArr PQ= sqrt (64+ (a^(2) + 16 + 8a)) `
`rArr a^(2) + 8a + 80 = 100 rArr a^(2) + 8a =20`
`rArr a^(2) + 10 a -2a -20=0`
`rArr (a-2)(a+ 10)=0 rArr (a=2) and (a=-10)`
`therfore " "a=2`