Slope question, easy 10 points?

Question

Please help me with the problem below.

Write an equation of the line described:

The perpendicular bisector of the segment joining (0,3) and (-4,5)

Thank you.

Answer 1

The general linear equation is y = mx + b where m is the slope and b is the y-intercept.

The segment has a y-intercept of 3 (where x = 0) and the slope is found by the rise/run of the two points given: (5 - 3) / (-4 - 0) = 2/-4 = -1/2. This yields the equation for the line segment of y = (-1/2) x + 3

The perpendicular of a line (or segment) has a slope that is the negative reciprocal of the line, in this case the slope of the perpendicular is +2/1 or 2.

Now you need to find the point that bisects the line segment. In this simple problem the easiest way is to take the half the difference of the x coordinates plus the starting x coordinate and the same for the y.  For x the mean is (0 + -4)/2 + 0 = -2 and for y it is (5 -3)/2 + 3 = 4. Which makes the bisecting point (-2, 4). You can check that this point sits on the line segment by using the y = (-1/2) x + 3 from above.

Now all you need is the y-intercept of the perpendicular. Remember that the slope of the perpendicular line is 2 and it passes through (-2, 4). This is easiest to see if you graph it out, but as x runs from -2 to 0, y rises from 4 to 8 (that's the definition of slope: rise/run). So the point (0, 8) is on the perpendicular line and x is zero which makes our y-intercept 8.

Put that all together and the equation for the perpendicular is y = 2x + 8.

Answer 2

First, find the slope of that line through the 2 points:

Slope = (5 - 3) / (-4 - 0)

Slope = 2/-4

Slope = -1/2

Next, find the midpoint:

(-4/2 , 8/2)

(-2,4)

Now, the perpendicular slope is the negative inverse of the slope we found before, which would be 2:

Now, using the point we found:

(y - 4) / (x + 2) = 2

Cross multiply:

y - 4 = 2(x + 2)

y - 4 = 2x + 4

y = 2x + 8

Answer 3

gradient of the line= (y2 -y1)/ (x2-x1)

= (3-5)/(0+4)

= -1/2

gradient of the perpendicular bisector is always the reciprocal and the prodouct of minus

therefore the gradient of the bisector= 2

the reason we find the midpoint is because thats the point where the perpendicular bisector meets the line

mid point= (-4/2,8/2)

= (-2,4)

y=mx + c

y=2x+c

(4)= 2(-2) + c

4= -4 +c

8=c

equation is

y=2x+8

good luck