Untitled-109

# Untitled-109 - PERPENDICULAR LINES If two lines of gradient...

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Unformatted text preview: PERPENDICULAR LINES If two lines of gradient m 1 and 1712 are perpendicular, then the product oftheir respective gradients must equal —1. ALTERNATIVELY the gradient of one line must equal the negative reciprocal of the other gradient. The concept is important later, particularly when determining equations of normals to curves. 7712 These two lines are at right angles to each other, In X771 2—1. m1 1 2 Example: Find the gradient of the line which is perpendicular to the line 3/ : inc—5. 3 4 Solution: Z x 2712 : —1 7712 —§ that is, the negative reciprocal. Example: Find the equation of the line passing through (5,—3) and which is perpendicular to x + 2 y + 6 = 0. Solution: x + 2 y + 6 = 0 {Rearrange into y = mx + b 2y —x—6 —1 y ?x~3 — 1 I711 ""— 2 to find the gradient m 1. Using y — y 1 = m (x — x 1) Since the lines are perpendicular, 2 (x _5) the gradient of this line must be 2, 1 y+3=2x—10 i.e. —§xm2=—1 y = 2x—13 [712 = 2 y-—3 = ...
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