Answer:
(x, y) = (2 35/74, 2 25/74)
Step-by-step explanation:
The closest point on the line to the given point will be the point of intersection of the given line and a perpendicular through the given point.
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A line perpendicular to ax+by+c=0 that goes through point (h, k) can be written as ...
b(x-h) -a(y-k) = 0
For the given line and point, the perpendicular line will be ...
7(x -2) +5(y -3) = 0
7x +5y -29 = 0
Using the cross-multiplication method, we can find the solutions to the system of equations consisting of these two lines. It will be ...
- -5x +7y -4 = 0
- 7x +5y -29 = 0
Δ = (-5)(5) -(7)(7) = -74
Δx = (7)(-29) -(5)(-4) = -183
Δy = (-4)(7) -(-29)(-5) = -173
x = Δx/Δ = -183/-74 = 2 35/74 ≈ 2.4730
y = Δy/Δ = -173/-74 = 2 25/74 ≈ 2.3378
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For more on the cross multiplication method, you can read ...
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