Find the point on the y-axis that is equidistant from (5 ,1) and (-3 -1). The answer is (0,4) but I don't know the process.
To find the point on the y-axis that is equidistant from two given points, we 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) is given by:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
In this case, one of the given points is (5, 1) and the other point is (-3, -1). Since we want to find the point on the y-axis, its x-coordinate will be 0, and we need to find its y-coordinate.
Let's calculate the midpoint between (5, 1) and (-3, -1):
Midpoint = ( (5 + (-3)) / 2 , (1 + (-1)) / 2 )
= (2 / 2, 0 / 2 )
= (1, 0)
So, the midpoint between (5, 1) and (-3, -1) is (1, 0). Since we are looking for a point on the y-axis, the x-coordinate will be 0. Therefore, the point on the y-axis that is equidistant from (5, 1) and (-3, -1) is (0, 0).
However, the answer you provided, (0, 4), is incorrect. Please double-check the question and the given points to ensure accuracy.
any point equidistant from the two given points must lie on the right bisector of the line joining the two points, so ...
midpoint of given points is (1,0)
slope of line joining the given points
= (-1-1)/(-3-5) = 1/4
so the slope of the right-bisector must be -4
equation of right-bisector:
y = -4x + b, but (1,0) lies on it, then
0 = -4 + b
b = 4
equation of right-bisector: y = 4x + 4
of course the y-intercept of y = mx+b is b
so the y-intercept is 4
or the point (0,4)