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.

Step-by-step 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.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.