# Find the point on the line -3 x + 3 y + 5 =0 which is closest to the point ( -4, 5 )?

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Find the point on the line -3 x + 3 y + 5 =0 which is closest to the point ( -4, 5 )

–3x + 3y + 5 = 0

3y = 3x – 5

y = x – 5/3

Find line perpendicular to given line passing through (–4, 5)

slope of perpendicular line = –1

(y – 5) = –1(x + 4)

y – 5 = –x – 4

y = –x + 1

Find intersection

x – 5/3 = –x + 1

2x = 8/3

x = 4/3

y = –(4/3) + 1

y = –1/3

Point which is closest = (4/3, –1/3)

• The shortest distance between 2 factors is a on the instant line. i could think of that in case you utilize a line that's perpendicular to 8x+6y-4=0 and passes by the factor (-3,-5) then you will discover that shortest distance. Then discover the factor that solves the two equations to discover the needed answer. The perpendicular line could be 4y=3x - 11. the answer (or intersection) to the two a sort of equations may be the factor they're searching for which i'm figuring to be (a million.sixty 4, -a million.fifty two) or while you're rounding your solutions to the closest 10th then (a million.6, -a million.5) additionally (8/5 , -3/2). wish this helped.