Question

REALLY NEED HELP FOR PART C PLEASE

Points P, Q and R have coordinates (-1, -3), (5, 7) and (7, -5) respectively. Find:
a the equation of the perpendicular bisector of PQ
b the equation of the perpendicular bisector of QR
c the exact coordinates of the point of intersection of the two perpendicular bisectors.

Answer 1

(-50,(28 2/3))

Explanation:

PQ's bisector is -3/5 and QR's bisector is 1/6

(-50,(28 2/3))

Answer 2

Explanation:

To find the equation of the perpendicular bisector of line segment PQ, we can use the midpoint formula to find the coordinates of the midpoint of PQ, and then use the slope formula to find the slope of the line. The midpoint formula is:

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

The slope formula is:

(y2 - y1)/(x2 - x1)

Plugging in the coordinates of points P and Q, we get:

Midpoint of PQ: ((-1 + 5)/2 , (-3 + 7)/2) = (2, 2)

Slope of PQ: (7 - (-3))/(5 - (-1)) = 10/6 = 5/3

Since the line perpendicular to PQ has a slope that is the negative reciprocal of the slope of PQ, the slope of the perpendicular bisector of PQ is -3/5.

We can now use the point-slope form of a linear equation to find the equation of the perpendicular bisector of PQ:

y - y1 = m(x - x1)

Plugging in the coordinates of the midpoint of PQ and the slope of the line, we get:

y - 2 = (-3/5)(x - 2)

This simplifies to:

y = (-3/5)x + (14/5)

So the equation of the perpendicular bisector of PQ is y = (-3/5)x + (14/5).

To find the equation of the perpendicular bisector of QR, we can use the same process. The midpoint of QR is ((7 + 5)/2 , (-5 + 7)/2) = (6, 1). The slope of QR is (7 - (-5))/(7 - 5) = 12/2 = 6/1 = 6. Therefore, the slope of the perpendicular bisector of QR is -1/6. Using the point-slope form of a linear equation, we get:

y - 1 = (-1/6)(x - 6)

This simplifies to:

y = (-1/6)x + (7/6)

So the equation of the perpendicular bisector of QR is y = (-1/6)x + (7/6).

To find the point of intersection of the two perpendicular bisectors, we can set the two equations equal to each other and solve for x. Doing so, we get:

(-3/5)x + (14/5) = (-1/6)x + (7/6)

This simplifies to:

(26/30)x = (7/6) - (14/5)

Solving for x, we get:

x = (42/30)

To find the y-coordinate of the point of intersection, we can substitute this value of x into either of the original equations and solve for y. Doing so, we get:

y = (-3/5)(42/30) + (14/5) = (84/30) - (42/5) = (-3/5)

Therefore, the exact coordinates of the point of intersection of the two perpendicular bisectors are (42/30, -3/5).