If R is the midpoint of PS with PR=6x+16 and RS=-26 then find PS

PS = 116

Step-by-step explanation:

Given:

PR = 6x + 16

RS = 12x - 26

Required:

Find PS

Solution:

Since R is the midpoint of PS, therefore,

PR = RS

6x + 16 = 12x - 26

Collect like terms

6x - 12x = -16 - 26

-6x = -42

Divide both sides by -6

x = -42/-6

x = 7

✔️PS = PR + RS (segment addition postulate)

PS = 6x + 16 + 12x - 26

Plug in the value of x

PS = 6(7) + 16 + 12(7) - 26

PS = 42 + 16 + 84 - 26

PS = 116

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.