Question

The point P is the foot of perpendicular from A(-5,7) to the line whose equation is 2x - 3y =+ 18 =0
Determine:
1.the equation of line AP
2.the coordinates of P
@jayzdd

Answer 1

we can first solve for y
2x - 3y = 18
2x - 18 = 3y
y = 2/3*x - 6

Answer 2

Slope of y = 2/3

Answer 3

what next?

Answer 4

so we know the given line, and teh point A(-5,7)
this is what we have so far graphically
https://www.desmos.com/calculator/x2ttl2ydj7

Answer 5

1. equation of line AP
we know the line is perpindicular, so the slope will be -3/2
and it goes through point (-5,7)
y - 7 = -3/2 * (x - (-5) )
simplify this

Answer 6

1. equation of line AP
we know the line is perpindicular, so the slope will be -3/2
and it goes through point (-5,7)
y - 7 = -3/2 * (x - (-5) )
simplify this
here is picture of perpindicular line
https://www.desmos.com/calculator/z5s2sepstl

Answer 7

y = -3/2*x - 15/2 + 7

Answer 8

y = -3/2*x - 15/2 + 7
y = -3/2*x - 1/2

Now find where the two lines intersect, that will be your foot P

Answer 9

y = -3/2*x - 15/2 + 7
y = -3/2*x - 1/2

Now find where the two lines intersect, that will be your foot P
solve \( y_1 = y_2\)
2/3*x - 6 = -3/2*x - 1/2

Answer 10

still there?

Answer 11

2/3*x + 3/2*x = 6 - 1/2
13/6 x = 11/2
x = 11/2 * 6 /13 = 33/13
the x value is 33/13
y value is -56/13