(2, 4)
Find the other endpoint of the line segment with the one endpoint (9,0) 1 poi
nd midpoint (2,0) *

The answer to your question is (-5, 0)

Step-by-step explanation:

Data

Endpoint = (9, 0)

Midpoint = (2, 0)

Endpoint 2 = ?

Formula

Xm = (x1 + x2) / 2

Ym = (y1 + y2) / 2

-Solve for x2 and y2

X2 = 2Xm - x1

Y2 = 2Ym - y1

-Substitution

X2 = 2(2) - 9

Y2 = 2(0) - 0

-Simplification

X2 = 4 - 9 = -5

Y2 = 0 - 0 = 0

-Coordinates of the endpoint 2

  (-5, 0)

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.

2

step-by-2step explanation: