Question

The diagonals XZ and WY of rectangle XYZW intersect at point M. If l(XZ) = 8 cm, find l(XM) and l(YM).

Answer 1

In rectangle XYZW, XY and ZW intersect at point M l(XZ)= 8 cm.
So, l(XM) = l (MZ) (Diagonals of a rectangle bisect each other )
l (XM) = $\frac{l\left(\mathrm{XZ}\right)}{2}$ = 4 cm
and l (YM) = l (MW) (Diagonals of a rectangle bisect each other )
l (YM) = $\frac{l\left(\mathrm{YW}\right)}{2}$
l (YW) = l (XZ) (Diagonals of a rectangle are congruent)
So, $\frac{l\left(\mathrm{YW}\right)}{2}$ = 4 cm
∴ l (XM) = 4 cm
l (YM) = 4 cm