For the given line segment, write the equation of the perpendicular bisector. a) y = 45 x + 1710b) y = 54 x + 1710c) y = 45 x + 4710d) y = -45 x - 4710

D) y = -4/5x – 47/10

Step-by-step explanation:

Step 1. Find the midpoint of the segment.

The two end points are (-6, -4) and (-2, 1).

The midpoint is at the average of the coordinates.

(xₚ, yₚ) = ((x₁ + x₂)/2, (y₁ + y₂)/2)

(xₚ, yₚ) = ((-6 - 2)/2, (-4 + 1)/2)

(xₚ, yₚ) = (-8/2, -3/2)

(xₚ, yₚ) = (-4, -3/2)

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Step 2. Find the slope (m₁) of the segment

m₁ = (y₂ - y₁)/(x₂ - x₁)

m₁ = (1 - (-4))/(-2 - (-6))

m₁ = (1 + 4)/(-2 + 6)

m₁ = 5/4

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Step 3. Find the slope (m₂) of the perpendicular bisector

m₂ = -1/m₁

m₂ = -4/5

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Step 4. Find the intercept of the perpendicular bisector

y = mx + b

y = -(4/5)x + b

The line passes through (-4, -3/2).

-3/2 = -(4/5)(-4) + b

-3/2 = 16/5 + b      Multiply each side by 10

 -15 = 32 + 10 b    Subtract 32 from each side

 -47 = 10b             Divide each side by 10

    b = -47/10

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Step 5. Write the equation for the perpendicular bisector

y = -4/5x – 47/10

The graph shows the midpoint of your segment at (-4, -3/2) and the perpendicular bisector passing through the midpoint and (0, -47/10).