Can someone help me find the point on the line −2x+2y−5=0 which is closest to the point (−3,−3)?

Answer 1

Well you want the perpendicular thru (-3,-3)

The given line is 2y = 5 + 2x

y = 5/2 + x

so the slope is 1.

Then the perpendicular line has slope -1, and it eats (-3,-3)

So it's intercept is -3 - (-3)(-1) = -3 - 3 = -6

Then the perpendicular line has equation y = -1x-6

THey meet at 5/2 + x = -x-6

2x = -6 - 5/2

2x = -12/2 - 5/2 = -17/2

x = -17/4

PLugging into these line equations:

(-1)(-17/4) - 6 = 17/4 - 6 = 17/4 - 24/4 = -7/4

5/2 + -17/4 = 10/4 + -17/4 = -7/4

(-17/4. -7/4)