Given quadrilateral rstu, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices. r(1, -3), s(4, -1), t(2, 2), u(-4, -2)

 The pair of parallel sides is (RS, TU) and the pairs of perpendicular sides are (RS, ST), (TU, ST).

Step-by-step explanation:  Given that RSTU is a quadrilateral, with vertices R(1, -3), S(4, -1), T(2, 2) and U(-4, -2).

We are given to determine the pair of parallel and perpendicular sides, if any, in quadrilateral RSTU.

We know that

two straight line are parallel if their slopes are equal and they are perpendicular if the product of their slopes is -1.

The slope of a straight line having points (a, b) and (c, d) on it is given by

So, the slopes of the sides RS, ST, TU and RS are calculated as follows :

We see that

So, the sides RS and TU are parallel.

And,

So, the sides ST is perpendicular to both RS and TU.

Thus, the pair of parallel sides is (RS, TU) and the pairs of perpendicular sides are (RS, ST), (TU, ST).

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following