A point is equidistant from (-2,4) and (3,5). It is also equidistant from (-2,-3) and (6,-1). Find the point
Please I need Help with this
To find the point that is equidistant from two given points, you can use the concept of the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Let's use this formula to find the midpoint of the first pair of points (-2, 4) and (3, 5):
Midpoint₁ = ((-2 + 3)/2, (4 + 5)/2)
= (1/2, 9/2)
Now, let's find the midpoint of the second pair of points (-2, -3) and (6, -1):
Midpoint₂ = ((-2 + 6)/2, (-3 + (-1))/2)
= (4/2, -4/2)
= (2, -2)
To find the point that is equidistant from both midpoints, we can use the same midpoint formula:
Point = ((Midpoint₁ + Midpoint₂)/2)
Substituting the values of Midpoint₁ and Midpoint₂, we get:
Point = (((1/2) + 2)/2, ((9/2) + (-2))/2)
= (5/4, 5/4)
Therefore, the point that is equidistant from the given pairs of points is (5/4, 5/4).