Question

Slope Criteria for Parallel and Perpendicular Lines: Mastery Test

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Arrange the pairs of points in order of the y-intercepts of their corresponding perpendicular bisectors, starting with the smallest and ending with


the largest.


A(-4,5) and B(8,9)


A(2, 4) and B(-8,6)


A(5, 4) and B(7.2)


A(2, 9) and B(-4.3)


A(3.-2) and B(9.-12)


A(4, 10) and B(8, 12)

Answer 1

below

Step-by-step explanation: Filler Also, I got it right

The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words,

Pick two points on the line and determine their coordinates.

Determine the difference in y-coordinates of these two points (rise).

Determine the difference in x-coordinates for these two points (run).

Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

The diagram below shows this method being applied to determine the slope of the line. Note that three different calculations are performed for three different sets of two points on the line.

Answer 2

Each of the points and the y-intercept of their perpendicular bisectors

1) A(-4,5) and B(8,9), y-intercept = 13

2) A(2, 4) and B(-8,6), y-intercept = 20

3) A(5, 4) and B(7.2), y-intercept = -3

4) A(2, 9) and B(-4.3), y-intercept = 5

5) A(3.-2) and B(9.-12), y-intercept = -10.6

6) A(4, 10) and B(8, 12), y-intercept = 23

Arranged in order of increasing y-intercepts of their perpendicular bisectors, from the smallest to largest y-intercept

5) A(3.-2) and B(9.-12), y-intercept = -10.6

3) A(5, 4) and B(7.2), y-intercept = -3

4) A(2, 9) and B(-4.3), y-intercept = 5

1) A(-4,5) and B(8,9), y-intercept = 13

2) A(2, 4) and B(-8,6), y-intercept = 20

6) A(4, 10) and B(8, 12), y-intercept = 23

Explanation:

The slopes of two perpendicular lines are related as thus

m₁m₂ = -1

Hence, for each of the two Points given, the slope of the perpendicular bisector is

m₂ = -(1/m₁)

But the slope of each of the lines connecting the two points is given as

m = (y₁ - y₂)/(x₁ - x₂)

And the coordinates of the midpoint, that the perpendicular bisector passes through is given as

(x, y) = {[(x₁ + x₂)/2], [(y₁ + y₂)/2]}

And from the slope of the perpendicular bisector and the coordinates of the midpoint of each question point, we can obtain the equation of the line that is the perpendicular bisector. And easily obtain the y-intercept from that.

Taking the points, one at time

1) A(-4,5) and B(8,9)

Slope of the line connecting the two points = m₁ = (9 - 5)/(8 - -4) = (4/12) = (1/3)

Slope of the perpendicular bisector

= m₂ = -1 ÷ (1/3) = -3

The midpoint of the two points is given as

= [(-4 + 8)/2, (9 + 5)/2]

= (2, 7)

The equation of the perpendicular bisector is then given as the equation of line with slope -3 and passes through (2, 7)

y = mx + c

7 = (-3×2) + c

7 = -6 + c

c = 7 + 6 = 13

y = -3x + 13

y-intercept = 13

2) A(2, 4) and B(-8,6)

Slope of the line connecting the two points = m₁ = (6 - 4)/(-8 - 2) = -(2/10) = -(1/5)

Slope of the perpendicular bisector

= m₂ = -1 ÷ -(1/5) = 5

The midpoint of the two points is given as

= [(2 + -8)/2, (4 + 6)/2]

= (-3, 5)

The equation of the perpendicular bisector is then given as the equation of line with slope 5 and passes through (-3, 5)

y = mx + c

5 = (5×-3) + c

5 = -15 + c

c = 5 + 15 = 20

y = 5x + 20

y-intercept = 20

3) A(5, 4) and B(7.2)

Slope of the line connecting the two points = m₁ = (2 - 4)/(7 - 5) = -(2/2) = -1

Slope of the perpendicular bisector

= m₂ = -1 ÷ -1 = 1

The midpoint of the two points is given as

= [(5 + 7)/2, (4 + 2)/2]

= (6, 3)

The equation of the perpendicular bisector is then given as the equation of line with slope 1 and passes through (6, 3)

y = mx + c

3 = (1×6) + c

3 = 6 + c

c = 3 - 6 = -3

y = x - 3

y-intercept = -3

4) A(2, 9) and B(-4.3)

Slope of the line connecting the two points = m₁ = (3 - 9)/(-4 - 2) = (-6/-6) = 1

Slope of the perpendicular bisector

= m₂ = -1 ÷ 1 = -1

The midpoint of the two points is given as

= [(2 + -4)/2, (9 + 3)/2]

= (-1, 6)

The equation of the perpendicular bisector is then given as the equation of line with slope -1 and passes through (-1, 6)

y = mx + c

6 = (-1×-1) + c

6 = 1 + c

c = 6 - 1 = 5

y = -x + 5

y-intercept = 5

5) A(3.-2) and B(9.-12)

Slope of the line connecting the two points = m₁ = (-12 - -2)/(9 - 3) = (-10/6) = -(5/3)

Slope of the perpendicular bisector

= m₂ = -1 ÷ (-5/3) = (3/5)

The midpoint of the two points is given as

= [(3 + 9)/2, (-2 + -12)/2]

= (6, -7)

The equation of the perpendicular bisector is then given as the equation of line with slope 3/5 and passes through (6, -7)

y = mx + c

-7 = [(3/5)×6] + c

-7 = 3.6 + c

c = -7 + -3.6 = -10.6

y = 3x/5 - 10.6

y-intercept = -10.6

6) A(4, 10) and B(8, 12)

Slope of the line connecting the two points = m₁ = (12 - 10)/(8 - 4) = (2/4) = (1/2)

Slope of the perpendicular bisector

= m₂ = -1 ÷ (1/2) = -2

The midpoint of the two points is given as

= [(4 + 8)/2, (10 + 12)/2]

= (6, 11)

The equation of the perpendicular bisector is then given as the equation of line with slope -2 and passes through (6, 11)

y = mx + c

11 = (-2×6) + c

11 = -12 + c

c = 11 + 12 = 23

y = -2x + 23

y-intercept = 23

1) A(-4,5) and B(8,9), y-intercept = 13

2) A(2, 4) and B(-8,6), y-intercept = 20

3) A(5, 4) and B(7.2), y-intercept = -3

4) A(2, 9) and B(-4.3), y-intercept = 5

5) A(3.-2) and B(9.-12), y-intercept = -10.6

6) A(4, 10) and B(8, 12), y-intercept = 23

Hope this Helps!!!