Find the coordinates of the other endpoint of the segment, given its midpoint M and one endpoint Q.
M(c, n), Q(h, s)
The second endpoint is P

P(2c - h, 2n - s )

Step-by-step explanation:

If there are two points (x1,y1) and (x2,y2) on the coordinate plane

then midpoint is given by (x1+x2)/2 , (y1+y2)/2

in the problem midpoint is m(c,n)

one point is Q(h,s)

let other point be P(x,y)

By using midpoint formula given above

for point P(x,y) and Q(h,s)

midpoint = (x+h)/2, (y+s)/2

also midpoint is m(c,n)

comparing m(c,n) with (x+h)/2, (y+s)/2

c = x+h/2

=> 2c = x+h

=> 2c - h = x

n = (y+s)/2

=> 2n = y+s

=> 2n - s = y

Thus, second endpoint is P(x,y) = P(2c - h, 2n - s )

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)