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Distance From A Point To A Line Page 398

Distance From A Point To A Line Page 398. Objective. To find the distance between a point and a line and the distance between two parallel lines. Formula. Remember that and ordered pair represents a point on the graph and is written in the form (x, y) The standard form of an equation is:

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Distance From A Point To A Line Page 398

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  1. Distance From A Point To A LinePage 398 Objective To find the distance between a point and a line and the distance between two parallel lines.

  2. Formula • Remember that and ordered pair represents a point on the graph and is written in the form (x, y) • The standard form of an equation is: A x + B y = c so, • D = Ax1 + By1 + c +√A² + B²

  3. Find the distance betweenP(3, -1) and the line with equation 2x + 5y –2 = 0 • d = Ax1 + By1 + C +√A² + B² • x1 = 3, y1 = -1, A = 2, B = 5, C = -2 • D = 2(3) + 5(-1) + (-2) +√2² + 5² • 6 + (-5) + (-2) √29 • -1 √29 • √29 or about –0.19 • 29

  4. Find the distance between the lines with equations 3x + 2y = 10 and y = 3/2 x + 7 Since y = 3/2 x + 7is in slope-intercept form, we know that (0, 7) are the coordinates of a point on the line So x = 0, y = 7, A = 3, B = 2 and C = -10 d = 3(0) + 2(7) + (-10) +√3² + 2² d = 14 – 10 √13 d = 4√13 or about 1.11 units 13

  5. Assignment • Page 402 – 403 • # 3 – 6, 15 - 22

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