Perpendicular Line Passing Through a Given Point
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Given two points (7,-2) and (-3,-10), we can determine the slope of the line passing through them as follows:
slope = (y2 - y1) / (x2 - x1)
slope = (-10 - (-2)) / (-3 - 7)
slope = -8 / -10
slope = 4 / 5
Since we want a line perpendicular to this line, we need to find its negative reciprocal. The negative reciprocal of 4/5 is -5/4.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the point (-8,-12), we can substitute the values into the equation:
y - (-12) = -5/4(x - (-8))
y + 12 = -5/4(x + 8)
Simplifying, we get:
y + 12 = -5/4x - 10
y = -5/4x - 22
Therefore, the equation of the perpendicular line passing through the point (-8,-12) is y = -5/4x - 22 in point-slope form.