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.

(D)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.

Step-by-step explanation:

Midpoint of SQ

Midpoint of PR

Now, we have established that the midpoints (point of bisection) are at the same point.

Two lines are perpendicular if the slope of one is the negative reciprocal of the other.

In option D

Therefore, lines RP and SQ are perpendicular.

Option D is the correct option.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

here is your mark brainliest