Question

On a coordinate plane, square p q r s is shown. point p is at (4, 2), point q is at (8, 5), point r is at (5, 9), and point s is at (1, 6). which statement proves that the diagonals of square pqrs are perpendicular bisectors of each other? the length of sp, pq, rq, and sr are each 5. the slope of sp and rq is negative four-thirds and the slope of sr and pq is three-fourths. the length of sq and rp are both startroot 50 endroot. the midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of rp is 7, and the slope of sq is negative one-sevenths.

Answer 1

A statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is: option D.

How to calculate the slope of a line?

Mathematically, the slope of a line is given by the following formula;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

For line RP, we have:

$Slope = \frac{9\;-\;2}{5\;-\;4}\\\\Slope = \frac{7}{1}$

Slope RP = 7.

For line SQ, we have:

$Slope = \frac{6\;-\;5}{1\;-\;8}\\\\Slope = \frac{1}{-7}$

Slope SQ = negative one-sevenths.

For the midpoint, we have:

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate = (8 + 1)/2 = 9/2 = 4.5.

Midpoint on y-coordinate = (9 + 2)/2 = 11/2 = 5.5.

In conclusion, a statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is that the midpoint of both diagonals is (4.5, 5.5), the slope of RP is 7, and the slope of SQ is negative one-sevenths.

Read more on squares here: https://brainly.com/question/2882032

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Answer 2

Answer:

Quandellious.

Step-by-step explanation: