Question

Determine the equation of the perpendicular bisector of the line through the points Q(5,8) and R(-1,2). Thanks c:

Answer 1

Preliminary steps: find the midpoint of the segment joining the two points, and find the slope of the line defined by the points. The slope of a perpendicular line is the opposite of the reciprocal of that slope. Use the point you found (the midpoint) and the perpendicular slope in the point slope form to define the desired line.

Answer 2

Can you do that?

Answer 3

What is the midpoint formula?

Answer 4

(x1 + x2) / 2) , (y1 + y2)/2)

Answer 5

Exactly. Average the x values, average the y values.

Answer 6

Thanks guys! So I got (2, 5). And is there any next steps? c:

Answer 7

now we need to make an equation, and to do that we need the slope
you can find the slope of the given line segment QR from the formula\[m={y_2-y_1\over x_2-x_1}\]

Answer 8

it turns out that a line perpendicular will have the negative reciprocal of that slope\[-\frac1m\]we then can use the midpoint you found, and the slope perpendicular to QR to make an equation
what is the slope of the line QR ?
what is the slope of the perendicular?

Answer 9

Do you use the end points of the line segment or..?

Answer 10

yeah, actually any two points on the line will work

Answer 11

...but since we are only given the endpoints that seems the logical choice

Answer 12

I got -6 over -6.

Answer 13

right, so the perpendicular is...?

Answer 14

1?

Answer 15

@TuringTest can u help me with a?

Answer 16

that is m, the slope of the line QR
what is the perpendicular? (I wrote the formula for the perpendicular to a slope above)

Answer 17

1 or -m?

Answer 18

Over*