Prove that ABCD is a rectangle. (Show all calculations)

Question

A(0;4), B(3;1), C(-3;-5), D(-6;-2) are the vertices of a quadrilateral in a Cartesian plane.

Answer 1

The vertices of a quadrilateral A (0, 4), B (3,1),C (-3,-5), D (-6,-2)

So opposite sides of quadrilateral have same length.

Now find the slopes of each side of quadrilateral.

we know that parallel lines have equal slope and perpendicular lines slopes are negitive recipracal to each other.

From the above we can able  to write angle between adjacent sides of qudraliteral is 90 degrees.

And oppsite sides are parallel.

Graph

Draw the coordinate plane.

Plot the above coordinate pairs.

Connect the plotted points.

Next connect the diagonals of quadrilateral.

From the graph we can observe the opposite sides of quadrilateral is parallel and same length.

All four angles of quadrilateral is right angles.

The diagonal of rectangle is congruent and bisect each other.

ABCD  is a rectangle.