Answer:
y = -1/7
Step-by-step explanation:
Mathematically, the distance between two points on a coordinate plane can be calculated using the formula;
d = √(x2-x1)^2 + (y2-y1)^2
for the first two points;
(5,y) and (1,4) ; we have
d = √(5-1)^2 + (y-4)^2
d = √(y-4)^2 + 16
For the other two;
(5,y) and (10,-3)
We have ;
d = √(5-10)^2 + (y + 3)^2
d = √(y+ 3)^2 + 25
from the question, these two distances are equal
all we have to do here is to equate the two distances
So we have it that;
(y-4)^2 + 16 = (y + 3)^2 + 25
y^2 -8y + 16 + 16 = y^2 + 6y + 9 + 25
-8y + 32 = 6y + 34
-8y -6y = 34-32
-14y = 2
y = -2/14
y = -1/7
