Question

for questions 8 and 9 , determine if S could lie an the perpendicular bisector ot bar (2R) with the give coordinates. 9. Q(-5,4),R(8,-3),5(-2,-5)

Answer 1

To determine if S lies on the perpendicular bisector of line segment QR, we find the midpoint of QR using the midpoint formula. Then, we calculate the distance between S and both Q and R using the distance formula. If the distances are equal, S lies on the perpendicular bisector; otherwise, it does not.

Step-by-step explanation:

To determine if point S could lie on the perpendicular bisector of line segment QR, we need to find the midpoint of QR and check if S is equidistant from both Q and R.

First, let's find the midpoint of QR using the formula:

Midpoint formula: (x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Using the given coordinates:

Q(-5, 4) and R(8, -3)

Calculating the midpoint:

(x, y) = [(-5 + 8)/2, (4 + (-3))/2]

(x, y) = [3/2, 1/2]

The midpoint of QR is (3/2, 1/2).

Now, let's calculate the distance between S and both Q and R using the distance formula:

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given coordinates:

S = (-2, -5)

Calculating the distance between S and Q:

d1 = sqrt((-2 - (-5))^2 + (-5 - 4)^2)

d1 = sqrt(9 + 81)

d1 = sqrt(90)

Calculating the distance between S and R:

d2 = sqrt((-2 - 8)^2 + (-5 - (-3))^2)

d2 = sqrt(100 + 4)

d2 = sqrt(104)

Since the distance from S to Q is not equal to the distance from S to R, S does not lie on the perpendicular bisector of QR.