Question

What is the y-coordinate of the point on the y-axis that is equidistant from points A(-2, 0) and B(-1, 4)?

a) -1

b) 1

c) 2

d) 4

Answer 1

The y-coordinate on the y-axis equidistant from points A(-2, 0) and B(-1, 4) is found by setting the distances from (0, y) to A and B equal and solving for y, which results in a coordinate of (0, 2).

Step-by-step explanation:

The y-coordinate of the point on the y-axis equidistant from points A(-2, 0) and B(-1, 4) can be found by setting the distance from the y-axis point, say (0, y), to both A and B equal.

Distance from (0, y) to A(-2, 0):
√((0 - (-2))^2 + (y - 0)^2) = √(4 + y^2)

Distance from (0, y) to B(-1, 4):
√((0 - (-1))^2 + (y - 4)^2) = √(1 + (y - 4)^2)

Set the distances equal:
√(4 + y^2) = √(1 + (y - 4)^2)

Square both sides:
4 + y^2 = 1 + (y - 4)^2

Expand and solve for y:
4 + y^2 = 1 + y^2 - 8y + 16

Cancel y^2 and simplify:
8y = 16 - 3

Divide by 8:
y = ⅓ = 2

The y-coordinate is therefore 2, which makes the answer (c) 2.