SOLUTION: The points that passes through the line (2,3) and is perpendicular to the line that passes through the points (4,5) and (9,12) ..?

Question 1024083: The points that passes through the line (2,3) and is perpendicular to the line that passes through the points (4,5) and (9,12) ..?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Gradient (slope) of line that passes through
(4,5) and (9,12)
Gradient (slope) = y2 - y1/x2 - x1
Gradient (slope) = 12 -5/9 - 4
Gradient (slope) = 7/5
Lines that are perpendicular to one another
have gradients (slopes) that multiply together
to give -1
m1 x m2 = -1
Using 7/5
7/5 x m2 = -1
m2 = -5/7
Setting up the line using the line equation
y - b = m(x - a)
m = -5/7 (a,b) = (2,3)
y - 3 = -5/7(x - 3)
y - 3 = -5/7x + 15/7
y = -5/7x + 15/7 + 21/7 (3)
y = -5/7x + 36/7
or multiply through by 7
7y = -5x + 36.
Points on this line can be:-
(3,3)
7y = -5(3) + 36
7y = -15 + 36
7y = 21
y = 3
(10,-2)
7y = -5x + 36
7y = -5(10) + 36
7y = -14
y = -2.
Hope this helps :-)
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