Question

Determine the value of p if A(-3;p) is equidistant from the points C(7;-1) and D(4;-4)

Answer 1

Use distance formula:
d = sqrt[(y2 - y1)^2 + (x2 - x1)^2]

Their distances from one point to (-3,p) must be the same, so
sqrt[(-1 - p)^2 + (7 - (-3))^2] = sqrt[(-4 - p)^2 + (4 - (-3))^2]
Square both sides:
(-1 - p)^2 + (7 + 3)^2 = (-4 - p)^2 + (4 + 3)^2
1 + 2p + p^2 + 100 = 16 + 8p + p^2 + 49

Now solve for p. Hope this helps~ `u`

Answer 2

p=6

Answer 3

thanks it helps me so much kamo

Answer 4

6

Answer 5

You're welcome! I'm glad I could help. If you have any other questions, feel free to ask.

Answer 6

Determine the value of P :A(-3;p) is equidistant from the points C(7;-1) and D(4;-4).

Answer 7

We can use the distance formula to determine the distance between point A and each of the other two points, C and D.

Distance between A and C:
d(A, C) = sqrt[(7 - (-3))^2 + (-1 - p)^2]
d(A, C) = sqrt[100 + (p - 1)^2]

Distance between A and D:
d(A, D) = sqrt[(4 - (-3))^2 + (-4 - p)^2]
d(A, D) = sqrt[49 + (p + 4)^2]

Since A is equidistant from C and D, we can set both distance equations equal to each other and solve for p.

sqrt[100 + (p - 1)^2] = sqrt[49 + (p + 4)^2]
Square both sides:
100 + (p - 1)^2 = 49 + (p + 4)^2
Simplify and solve for p:
51 = 18p + 16
35 = 18p
p = 35/18

Therefore, the value of p is 35/18.