The equation from the origin to the midpoint of the given points works out as y = 1/8x whereas 1/8 is the slope and there is no y intercept.
the origin and it has the coordinates of (0,0)
Points: (13, 17) and (19, 23) Midpoint: (16, 20) Slope of required equation: 5/4 Its equation: 4y = 5x or as y = 1.25x Its distance from (0, 0) to (16, 20) = 4 times sq rt 41
Points: (2, 5) and (11, 17) Midpoint: (6.5, 11) Slope: 4/3 Perpendicular slope: -3/4 Perpendicular equation: y-11 = -3/4(x-6.5) => 4y = -3x+63.5 In its general form: 3x+4y-63.5 = 0
Points: (-2, 2) and (6, 4) Midpoint: (2, 3) Slope: 1/4 Perpendicular slope: -4 Perpendicular bisector equation: y-3 = -4(x-2) => y = -4x+11
Points: (13, 19) and (23, 17) Midpoint: (18, 18) Slope: -1/5 Perpendicular slope: 5 Perpendicular equation: y-18 = 5(x-18) => y = 5x-72
Points: (7, 3) and (-6, 1) Midpoint: (0.5, 2) Slope: 2/13 Perpendicular slope: -13/2 Perpendicular equation: y-2 = -13/2(x-0.5) => 2y-4 = -13x+6.5 => 2y = -13x+10.5
Here are the key steps:* Find the midpoint of the given line. * Find the slope of the given line. * Divide -1 (minus one) by this slope, to get the slope of the perpendicular line. * Write an equation for a line that goes through the given point, and that has the given slope.
Points: (7, 3) and (-6, 1) Midpoint: (0.5, 2) Slope: 2/13 Perpendicular slope: -13/2 Perpendicular equation: y-2 = -13/2(x-0.5 => 2y = -13x+10.5
Points: (7, 3) and (-6, 1) Midpoint: (0.5, 2) Slope: 2/13 Perpendicular slope: -13/2 Perpendicular bisector equation: y-2 = -13/2(x-0.5) => 2y = -13x+10.5
Points: (0, 5) and (3, 0) Midpoint: (1.5, 2.5) Slope: -5/3 Perpendicular slope: 3/5 Perpendicular equation: y--5 = 3/5(x--3) => 5y = 3x-16 Distance is the square root of (1.5--3)^2+(2.5--5)^2 = 8.746 to three decimal places
Draw one square. Join the midpoint of each side to the midpoint of the adjacent sides. The resulting figure meets the requirements.
Midpoint: (-3/2, -1) Gradient or slope: 8 Perpendicular slope: -1/8 Equation: y- -1 = -1/8(x- -3/2) y = -1/8x -3/16 -1 y = -1/8x -19/16 The perpendicular equation can be expressed in the form of: 2x+16y+19 = 0