Question

Using the digits 1 to 9, at most one time each, fill in the boxes so that the points make a parallelogram. Mathematically, use parallel line or congruent sides to explain your answer. If there are calculations, include those in your explanation.

Answer 1

Answer:

$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

Step-by-step explanation:

The coordinates are:

$\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right$

The parallelogram is attached below.

To verify if these coordinates form a parallelogram, we show that:

• AB=CD; and
• AC=BD

Using Distance Formula

$AB = \sqrt{(6-8)^2+(9-3)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} units$

$CD = \sqrt{(2-4)^2+(7-1)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} units$

$AC = \sqrt{(8-4)^2+(3-1)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} units$

$BD = \sqrt{(6-2)^2+(9-7)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} units$

Since AB=CD; and AC=BD, the coordinates A, B, C, and D form the vertex of a parallelogram.