Question

Sammy is classifying quadrilateral EFGH. How can she use coordinate geometry to determine whether EFGH is a rectangle?

E(7, 10), F(4, 7), G(6, 5), H(9, 8)

Sammy can use the distance formula to show opposite sides are equal and the slope formula to show that consecutive sides have opposite reciprocal slopes.

Sammy can use the distance formula to show opposite are perpendicular and the slope formula to show that consecutive sides are equal.

Sammy can use the distance formula to show that all sides are equal and the slope formula to show that consecutive sides have the same slope.

Sammy can use the distance formula to show that all sides are parallel and the slope formula to show that consecutive sides are equal.

Answer 1

Remember, a rectangle has two pairs of sides that are congruent and parallel

Congruent means that they're equal
Parallel means they have the same slope
Perpendicular means the slopes are opposite reciprocal

Be careful about the answer choices

A square has all equal sides
A rectangle has two pairs of equal sides

Answer 2

Do the opposite sides have parallel slopes or perpendicular slopes?
What about the consecutive sides?

Answer 3

These are opposite sides

Answer 4

These are consecutive sides

Answer 5

Ok so i think it is the first one " Sammy can use the distance formula to show opposite sides are equal and the slope formula to show that consecutive sides have opposite reciprocal slopes."

Answer 6

Good job! That is correct :)