Finding equation of a line

[wicked bloom]

I'm doing this problem and I get y-2 = 2(x-3) or y-4 = 2(x+1), but the answer sheet says otherwise. I'm confused as to how they get this answer?

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[wicked bloom]

Answer sheet answer:

[keen moth]

Step 1) Find the midpoint of AB:

x-coordinate : (-1 + 3)/2 = 1 y-coordinate: (4 + 2)/2 = 3 Midpoint (1,3)

Step #2) Find the slope, slope is rise over run, or (Y2 - Y1) / (X2 - X1)

(2 - 4) / (3 - -1) = -2/4 = -1/2

Step 3) Find perpendicular slope, take the reciprocal and multiply by -1: +2/1 = 2

Step 4) pick form of equation

4a) point-slope form: Y - 3 = 2(X -1)

4b) slope-intercept form also called y = mx + b form

y = 2x +b to find b substitute in the values for x(1) and y(3) so….

3 = (2)(1) + b => 3 = 2 + b subtract 2 from both sides, 1 = b

y = 2x +1

[elder pecan]

your answers are of the equation of just that line, you need the perpendicular bisector

[calm terrace]

nah they did take the negative inverse of the slope just not moved over the midpoint

[elder pecan]

oh yea slope is correct

[rocky spire]

It gives y-3=2(x-2)

[elder pecan]

midpoint?

[calm terrace]

1 is the average of 3 and -1

so 2(x-1) is right

[elder pecan]

yup

except your answer wants to use x and not n

[rocky spire]

🤡

[calm terrace]

that’s probably a handwritten x

[wicked bloom]

thank you