Line t passes through points (8, 10) and (1, 2). Line u is perpendicular to t. What is the slope of line u?Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Question
Line t passes through points (8, 10) and (1, 2). Line u is perpendicular to t. What is the slope of line u?Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Solution
To find the slope of line u, we first need to find the slope of line t. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points (8, 10) and (1, 2) into the formula, we get:
m = (2 - 10) / (1 - 8) = -8 / -7 = 8/7
This is the slope of line t.
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. The reciprocal of 8/7 is 7/8, so the slope of line u is -7/8.
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