Mathematics

Problem

Four points are to be plotted to form a rectangle on the Cartesian plane. a. (i) Plot the points

A(1,2)

B(1,7)

C(6,7)

and

D(6,2)

on graph paper and join them in order. b. (ii) After drawing the rectangle, determine the coordinates of the midpoint

M

of diagonal

AC

by reading directly from your graph. c. (iii) Reflect point

D

in the

y

-axis to obtain point

D'

. Use your graph to write the coordinates of

D'

. d. (iv) Without using any algebraic formula, explain how the graph confirms that

ABCD

is a rectangle.

Intuitive explanation

A rectangle is defined by having four right angles and opposite sides that are equal and parallel. The key insight is that once you choose one corner and decide on the length and width, the other three corners are completely determined—you just need to move horizontally and vertically from your starting point. Think of it as building outward: pick a starting point, go right (or left) by some distance, then go up (or down) by another distance, then complete the opposite corner by combining those two movements.

Intuitive explanation

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