Question

If (x, y) lies on the line joining the two points (1, - 3) and (-4 , 2), prove that x + y + 2 =0

Answer 1

$\bold{\underline{\underline{PROOF}}}$

$First, find its slope. \\ \\ Slope \ = \frac{y_1 - y_2}{x_1 - x_2} = \frac{(-3)-2}{1-(-4)} = \frac{-3-2}{1+4} = \frac{-5}{5} =\ -1 \\ \\ \therefore\ Slope \ = -1$

$Let \ (x, y)\ be a point on the line. \\ \\ Consider \ (x, y)\ and \ (1, -3). \\ \\ \\ Slope \\ \\ = \frac{y - (-3)}{x - 1} = -1 \\ \\ = \frac{y + 3}{x - 1} = -1 \\ \\ \\ y + 3 =\ -1(x - 1) \\ \\ y + 3 = - x + 1 \\ \\ y + 3 + x - 1 = 0 \\ \\ x + y+ 3 - 1 = 0 \\ \\ x + y + 2 = 0 \\ \\ \\ Hence proved.$

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