Answer:
The other endpoint is located at (-4,-2)
Step-by-step explanation:
we know that
The diagonals of a rhombus bisect each other
That means-----> The diagonals of a rhombus intersect at the midpoint of each diagonal
so
The point (0,4) is the midpoint of the two diagonals
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
we have
[tex]M=(0,4)[/tex]
[tex](x_1,y_1)=(4,10)[/tex]
substitute
[tex](0,4)=(\frac{4+x_2}{2},\frac{10+y_2}{2})[/tex]
Find the x-coordinate [tex]x_2[/tex] of the other endpoint
[tex]0=\frac{4+x_2}{2}[/tex]
[tex]x_2=-4[/tex]
Find the y-coordinate [tex]y_2[/tex] of the other endpoint
[tex]4=\frac{10+y_2}{2}[/tex]
[tex]8=10+y_2[/tex]
[tex]y_2=-2[/tex]
therefore
The other endpoint is located at (-4,-2)
