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The line through (x,-6) and (-2,-1) is perpendicular to a line with slope -2 . Find x.

1212. The line through (x,−6) (x,-6) and (−2,−1) (-2,-1) is perpendicular to a line with slope −2-2 . Find x x .

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Full solution

Q. 1212. The line through (x,−6) (x,-6) and (−2,−1) (-2,-1) is perpendicular to a line with slope −2-2 . Find x x .
  1. Calculate slope: Find the slope of the line through (x,−6)(x, -6) and (−2,−1)(-2, -1) using the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.\newlinem=−1−(−6)−2−xm = \frac{-1 - (-6)}{-2 - x}\newlinem=5−2−xm = \frac{5}{-2 - x}
  2. Determine perpendicular slope: Since the line is perpendicular to a line with slope −2-2, the slope of our line is the negative reciprocal of −2-2.\newlinem=12m = \frac{1}{2}
  3. Set up equation: Set the slope of our line equal to the negative reciprocal of −2-2.\newline5(−2−x)=12\frac{5}{(-2 - x)} = \frac{1}{2}
  4. Cross multiply: Cross multiply to solve for xx.5×2=1×(−2−x)5 \times 2 = 1 \times (-2 - x)10=−2−x10 = -2 - x
  5. Isolate xx: Add 22 to both sides to isolate xx.\newline10+2=−x10 + 2 = -x\newline12=−x12 = -x
  6. Solve for x: Multiply both sides by −1-1 to solve for x.\newlinex=−12x = -12

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