Question

17. a) Show that the diagonals of the quadrilateral formed by the
vertices (-1, 2), (5, 4), (3, 4) and (-3, 2) taken in order,
bisect each other.

Answer 1

Answer:

AC and BD are diagonals

Answer 2

Therefore the diagonals bisect each other.

Step-by-step explanation:

Bisect: Divided two equal part of a line segment.

Given vertices of the quadrilateral are A(-1,2),B(5,4), C(3,4) and D(-3,2)

Here the diagonals of the quadrilateral is AC and BD.

If there mid-point are same then the diagonals bisect each other.

If $(x_1,y_1)$ and $(x_2,y_2)$ are two points.

Then the co-ordinate of mid-point is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Therefore the mid-point of AC is $(\frac{-1+3}{2},\frac{2+4}{2})$ =(1,3)

The mid-point of BD is $(\frac{5-3}{2},\frac{4+2}{2})$ = (1,3)

Since the mid point of AC and BD is same.

Therefore the diagonals bisect each other.