Question

The line that passes through the points (5, 3)

and (8. A) is perpendicular to the line
6x + 7y + 13 = 0. Determine the value of A.

Answer 1

`(13)/(2)`

Explanation:

slope of the line that passes thru (5, 3) and (8, A)

`= (a - 3)/(8 - 5) \\ (a - 3)/(3)`

the line that is perpendicular to the given line is

6x + 7y + 13= 0

finding the slop of this line :-

`6x + 7y + 13 = 0 \\ 7y = - 6x - 13 \\ y = - (6)/(7) x - (13)/(7)`

Comparing with standard equation of a line

y = mx + c

• where m is the slop and c is the y- intercept

m = - 6/ 7

Since, the two lines are perpendicular to each other the product of their slopes will be - 1

`(a - 3)/(3) * ( - 6)/(7) \\ ( - 2(a - 3))/(7) = - 1 \\ - 2a + 6 = - 7 \\ - 2a = - 7 - 6 \\ - 2a = - 13 \\ 2a = 13 \\ a = (13)/(2)`

( canceling the 2 negative signs on both the sides )