Question

Which of the following points is an equal distance (equidistant) from A(−4, 1) and B(2, −3)?

J(−3, −4)

K left parenthesis negative start fraction three over two end fraction comma negative start fraction one over two end fraction right parenthesis

L(−1, −2)

N(4, 1)

Answer 1

Using your answer choices, (3, 0) satisfies the resulting equation.

Explanation:

Even if we did not know the choices, we can still use algebra to find the coordinate point(s). We can use the distance formula.

d = √[(x1 - x2)2 + (y1 - y2)2]

where:

d = distance

(x1 , y1) and (x2 , y2) are given points.

Since we need to find the point that has he same distance between the points, we will use the distance formula and equated them.

Let (x3, y3) be the point we need to find. So by using the distance formula, we have

√[(0 - x3)2 + (-4 - y3)2] = √[(-2 - x3)2 + (0 - y3)2]

Squaring both sides of the equation leaves us with

x32 + (-4 - y3)2 = (-2 - x3)2 + y32

x32 + (-4 - y3)(-4 - y3) = (-2 - x3)(-2 - x3) + y32

x32 + 16 + 8y3 + y32 = 4 + 4x3 + x32 + y32

Eliminating x32 and y32

16 + 8y3 = 4 + 4x3

Move all the terms to the left side of equation to make the right side equal to zero.

16 + 8y3 - 4 - 4x3 = 0

12 + 8y3 - 4x3 = 0

Factoring, we get

4(3 + 2y3 - x3) = 0

3 + 2y3 - x3 = 0

2y3 - x3 = -3

Using your answer choices, (3, 0) satisfies the resulting equation.