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What is the perpendicular distance from the point 7 5 that meets the line of 4 1 and 0 4 at right angles on the Cartesian plane showing key aspects of work?
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∙ 9y ago
Points: (4, 1) and (0, 4)
Slope: -3/4
Equation: 4y = -3x+16
Perpendicular slope: 4/3
Perpendicular equation: 3y = 4x-13
Both equations meet at: (4, 1) from (7, 5) at right angles
Perpendicular distance: square root of [(4-7)squared+(1-5)squared)] = 5 units
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∙ 9y ago
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What is rhe perpendicular distance from the point 4 8 to the line of y equals 2x plus 10 on the Cartesian plane showing key aspects of work with an answer to an appropriate degree of accuracy?
Equation: y = 2x+10 and slope is 2 Perpendicular slope: -1/2 Perpendicular equation: 2y = -x+20 Both equations intersect at: (0, 10) from (4, 8) Distance: square root of (0-4)^2 plus (10-8)^2 = 4.472 to three decimal places
What is the perpendicular distance from the point of 2 4 to the equation y equals 2x plus 10 on the Cartesian plane showing work?
Equation: y = 2x+10 Point: (2, 4) Perpendicular slope: -1/2 Perpendicular equation: y-4 = -1/2(x-2) => 2y = -x+10 Both equations intersect at: (-2, 6) Using distance formula: (2, 4) to (-2, 6) = 2 times square root of 5
What is the perpendicular distance from the point 19 29 that meets the straight line equation 3y equals 9x plus 18 on the Cartesian plane showing work and answer to an appropriate degree of accuracy?
If: 3y = 9x+18 then y = 3x+6 with a slope of 3 Perpendicular slope: -1/3 Perpendicular equation: y-29 = -1/3(x-19) => 3y = -x+106 Both equations intercept at: (8.8, 32.4) Perpendicular distance: square root of (8.8-19)^2+(32.4-29)^2 = 10.75 rounded
What is the distance from the point 5 7 that is perpendicular to to the straight line equation of 3x-y plus 2 equals 0 on the Cartesian plane showing key aspects of work?
To find the perpendicular distance from a given point to a given line, find the equation of the line perpendicular to the given line which passes through the given point. Then the distance can be calculated as the distance from the given point to the point of intersection of the two lines, which can be calculated by using Pythagoras on the Cartesian coordinates of the two points. A line in the form y = mx + c has gradient m. If a line has gradient m, the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m (the negative reciprocal of the gradient). A line through a point (x0, y0) with gradient m has equation: y - yo = m(x - x0) Thus the equation of the line through (5, 7) that is perpendicular to 3x - y + 2 = 0 can be found. The intercept of this line with 3x - y + 2 = 0 can be calculated as there are now two simultaneous equations. → The perpendicular distance from (5, 7) to the line 3x - y + 2 = 0 is the distance form (5, 7) to this point of interception, calculated via Pythagoras: distance = √((change_in_x)^2 + (change_in_y)^2) This works out to be √10 ≈ 3.162
What is the equation and its perpendicular distance from the point -3 -5 whose line meets the line of 0 5 to 3 0 at its midpoint on the Cartesian plane showing work?
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
What is rhe perpendicular distance from the point 4 8 to the line of y equals 2x plus 10 on the Cartesian plane showing key aspects of work with an answer to an appropriate degree of accuracy?
Equation: y = 2x+10 and slope is 2 Perpendicular slope: -1/2 Perpendicular equation: 2y = -x+20 Both equations intersect at: (0, 10) from (4, 8) Distance: square root of (0-4)^2 plus (10-8)^2 = 4.472 to three decimal places
What is the perpendicular bisector equation that meets the line 13 19 and 23 17 at midpoint on the Cartesian plane showing all aspects of work with answer?
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
What is the perpendicular distance from the point of 2 4 to the equation y equals 2x plus 10 on the Cartesian plane showing work?
Equation: y = 2x+10 Point: (2, 4) Perpendicular slope: -1/2 Perpendicular equation: y-4 = -1/2(x-2) => 2y = -x+10 Both equations intersect at: (-2, 6) Using distance formula: (2, 4) to (-2, 6) = 2 times square root of 5
What is the perpendicular distance from the point 19 29 that meets the straight line equation 3y equals 9x plus 18 on the Cartesian plane showing work and answer to an appropriate degree of accuracy?
If: 3y = 9x+18 then y = 3x+6 with a slope of 3 Perpendicular slope: -1/3 Perpendicular equation: y-29 = -1/3(x-19) => 3y = -x+106 Both equations intercept at: (8.8, 32.4) Perpendicular distance: square root of (8.8-19)^2+(32.4-29)^2 = 10.75 rounded
What is the distance from the point 5 7 that is perpendicular to to the straight line equation of 3x-y plus 2 equals 0 on the Cartesian plane showing key aspects of work?
To find the perpendicular distance from a given point to a given line, find the equation of the line perpendicular to the given line which passes through the given point. Then the distance can be calculated as the distance from the given point to the point of intersection of the two lines, which can be calculated by using Pythagoras on the Cartesian coordinates of the two points. A line in the form y = mx + c has gradient m. If a line has gradient m, the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m (the negative reciprocal of the gradient). A line through a point (x0, y0) with gradient m has equation: y - yo = m(x - x0) Thus the equation of the line through (5, 7) that is perpendicular to 3x - y + 2 = 0 can be found. The intercept of this line with 3x - y + 2 = 0 can be calculated as there are now two simultaneous equations. → The perpendicular distance from (5, 7) to the line 3x - y + 2 = 0 is the distance form (5, 7) to this point of interception, calculated via Pythagoras: distance = √((change_in_x)^2 + (change_in_y)^2) This works out to be √10 ≈ 3.162
What is the equation and its perpendicular distance from the point -3 -5 whose line meets the line of 0 5 to 3 0 at its midpoint on the Cartesian plane showing work?
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
What is the perpendicular distance from the point of 2 4 on the Cartesian plane to the straight line equation of y equals 2x plus 10 showing key stages of work?
1 Equation: y = 2x+10 2 Perpendicular equation works out as: 2y = -x+10 3 Point of intersection: (-2, 6) 4 Distance is the square root of: (-2-2)2+(6-4)2 = 2 times sq rt of 5
What is the perpendicular distance from the point of 7 and 5 that meets the straight line equation of 3x plus 4y equals 0 on the Cartesian plane showing work?
Equation: 3x+4y = 0 => y = -3/4x Perpendicular slope: 4/3 Perpendicular equation: 4x-3y-13 = 0 Equations intersect at: (2.08, -1.56) Distance from (7, 5) to (2.08, -1.56) = 8.2 units using the distance formula
What is the perpendicular distance from the point 4 -2 to the line 2x -y -5 equals 0 showing key stages of work?
Points: (4, -2) Equation: 2x-y-5 = 0 Perpendicular equation: x+2y = 0 Equations intersect at: (2, -1) Perpendicular distance is the square root of: (2-4)2+(-1--2)2 = 5 Distance = square root of 5
What is the perpendicular distance from the coordinate 11 and 17 that meets the equation 3x plus 4y-63.5 equals 0 on the Cartesian plane showing work with answers?
Coordinate: (11, 17)If: 3x+4y-63.5 = 0Then: 4y = -3x+63.5 => y = -3/4x+15.875Slope: -3/4Perpendicular slope: 4/3Perpendicular equation: y-17 = 4/3(x-11) => 3y = 4x+7Both equations intersect at: (6.5, 11)Perpendicular distance: square root of [(6.5-11)^2+(11-17)^2] = 7.5
What is the perpendicular distance from the coordinate of 2 5 that meets the staight line of y equals 7x plus 13 at right angles on the Cartesian plane showing all work and answer to 3 decimal places?
Coodinate: (2, 5) Equation: y = 7x+13 Slope: 7 Perpendicular slope: -1/7 Perpendicular equation: 7y = -x+37 Both equations intersect at: (-1.08, 5.44) Perpendicular distance: square root of [(-1.08-2)^2+(5.44-5)^2] = 3.111 to 3 d.p.
What is the perpendicular distance from the point 7 5 to the staight line equation 3x plus 4y -16 equals 0 showing key stages of work?
Equation: 3x+4y-16 = 0 Perpendicular equation: 4x-3y-13 = 0 Both equations intersect at: (4, 1) Perpendicular distance: square root of (7-4)2+(5-1)2 = 5
