Question

Hiep is writing a coordinate proof to show that the midsegment of a trapezoid is parallel to its bases. He starts by assigning coordinates as given, where RS¯¯¯¯¯ is the midsegment of trapezoid KLMN .

Trapezoid K L M N on the coordinate plane. The vertices of the trapezoid are K begin ordered pair 0 comma 0 end ordered pair, L begin ordered pair 2a comma 0 end ordered pair, M begin ordered pair 2d comma 2c end ordered pair, and N begin ordered pair 2b comma 2c end ordered pair. Segment R S is drawn with point R on segment K N and point S on segment L M.

Drag and drop the correct answers to complete the proof.

Since RS¯¯¯¯¯ is the midsegment of trapezoid KLMN , the coordinates of R are (b,) and the coordinates of S are (, c).

The slope of KL¯¯¯¯¯ is .

The slope of RS¯¯¯¯¯ is 0.

The slope of NM¯¯¯¯¯¯¯ is 0.

The slope of each segment is 0; therefore, the midsegment is parallel to the bases.

Answer 1

Explanation:

Given that KLMN is a trapezium.

K has coordinates (0,0), L(2a,0), M(2d,2c) and N(2b,2c)

R is the mid point of KN

Hence coordinates of R will be using mid point formula (x1+x2/2, y1+y2/2)

= (a,c)

Similarly S is mid point of segment LM.

Hence S = (a+d,c)

The slope of SL is = (y2-y1)/(x2-x1) = (a-d)/-c=(d-a)/c

The slope of RS = (c-c)/d =0

The slope of NM = (2c-2c)/(2b-2d) = 0

Since slope of RS = slope of NM

We get RS is parallel to NM

Already NM is parallel to KL because bases of trapezium

Hence RS is parallel to both the bases.