A is the point (-4,5) and B is the point (5,8). The perpendicular to the line AB at point A crosses the y axis at point C. Find the coordinates of C.

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A is the point (-4,5) and B is the point (5,8). The perpendicular to the line AB at point A crosses the y axis at point C. Find the coordinates of C.

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facundo3141592 facundo3141592 · Answer 1 · 2025-03-31T09:37:24-04:00

Answer: Point C is (0, -7)

Step-by-step explanation:

For a general line y = a*x +b

A perpendicular line to this one will have a slope equal to -(1/a)

First, for a line y = a*x + b that passes through points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Then for a line that passes through the points A (-4, 5) and B (5, 8) the slope is:

a = (8 - 5)/(5 - (-4)) = 3/9 = 1/3

a = 1/3

Then, a line perpendicular to this one will have the slope:

a' = -(1/(1/3) = -3

Then the perpendicular line is something like:

y = -3*x + b

Now we know that this line passes through point A, then when x = -4, we have y = 5

if we replace these values we get:

5 = -3*(-4) + b

5 = 12 + b

5 - 12 = b

-7 = b

Then our line is:

y = -3*x - 7

This line intersects the y-axis at point C, we know that the y-axis corresponds to x = 0.

Then:

y = -3*0 - 7

y = -7

The point C is (0, -7)