Final answer:
To determine which of the given points is equidistant to point A and point B, we can find the distance between each point and both A and B using the distance formula. By comparing the distances, we can identify the point that is equidistant to A and B. The point that satisfies this condition is option a) C(-7, 3).
Step-by-step explanation:
To determine which of the following points is equidistant to point A(2, -8) and point B(-5, -2), we need to find the distance between each point and both A and B. We can use the distance formula, which is the square root of the sum of the squares of the differences in x-coordinates and y-coordinates. We will calculate the distance for each point:
a) C(-7, 3):
Distance to A: sqrt(((-7-2)^2 + (3-(-8))^2) = sqrt(81 + 121) = sqrt(202)
Distance to B: sqrt(((-7-(-5))^2 + (3-(-2))^2) = sqrt(4 + 25) = sqrt(29)
b) D(-9, 7):
Distance to A: sqrt(((-9-2)^2 + (7-(-8))^2) = sqrt(121 + 225) = sqrt(346)
Distance to B: sqrt(((-9-(-5))^2 + (7-(-2))^2) = sqrt(16 + 81) = sqrt(97)
c) E(-11, 12):
Distance to A: sqrt(((-11-2)^2 + (12-(-8))^2) = sqrt(169 + 400) = sqrt(569)
Distance to B: sqrt(((-11-(-5))^2 + (12-(-2))^2) = sqrt(36 + 196) = sqrt(232)
d) F(-2, 1):
Distance to A: sqrt(((-2-2)^2 + (1-(-8))^2) = sqrt(16 + 81) = sqrt(97)
Distance to B: sqrt(((-2-(-5))^2 + (1-(-2))^2) = sqrt(9 + 9) = sqrt(18)
From the calculations, we can see that point C has the same distance to A and B, making it equidistant to both points. Therefore, the correct answer is a) C(-7, 3).