The diagonals of a rhombus intersect at the point (0,4). If one endpoint of the longer diagonal is located at point (4,10), where is the other endpoint located?
Accepted Solution
A:
Answer:The other endpoint is located at (-4,-2)Step-by-step explanation:we know thatThe diagonals of a rhombus bisect each otherThat means-----> The diagonals of a rhombus intersect at the midpoint of each diagonalsoThe 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]thereforeThe other endpoint is located at (-4,-2)