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.

A

Step-by-step explanation:

in a rectangle opposite sides are equal.

Adjacent sides are perpendicular, hence slopes of adjacent sides are reciprocal to each other.

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.

Step-by-step explanation:

A rectangle is define as a figure which have all right angles and each pair of opposite sides are equal. So, to determine if the given figure is a rectangle, Sammy needs to demonstrate these two characteristics, because they define rectangles.

So, the best way to do it is option A, because involves using a distance formula to demonstrate the equality of opposite sides, which is the number one characteristic. And then involves using the slope formula to demonstrate that consecutive sides have opposite reciprocal slopes, which would mean that each angle is equal to 90°, because when to lines have opposite and reciprocal slopes is because there's a right angle between them.