Question

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Answer 1

Answer:-

10x+6y=3910x+6y=39

Further Explanation:

Step 1

we have

R(-1,5), S(1,8), T(7,-2), and U(2,0)

Remember that the median of a trapezoid is a segment that joins the midpoints of the nonparallel sides.

Plot the trapezoid

See the attached figure

In this problem, the non parallel sides are RS and TU

Step 2

Find the midpoint RS

The midpoint of segment RS is equal to the formula

$\frac{x1+x2}{2},\frac{y1+y2}{2}$

we have

R(-1,5), S(1,8)

Substitute the values

$\frac{-1+1}{2},\frac{5+8}{2}$

(0,6.5)(0,6.5)

Step 3

Find the midpoint TU

The midpoint of segment RS is equal to the formula

$\frac{x1+x2}{2},\frac{y1+y2}{2}$

we have

T(7,-2), U(2,0)

Substitute the values

$\frac{7+2}{2},\frac{-2+0}{2}$

(4.5,-1)(4.5,−1)

Step 4

Find the equation of the line containing the median

we have the points

(0,6.5), (4.5,-1)(0,6.5),(4.5,−1)

Find the slope m

m=(-1-6.5)/(4.5-0)=-5/3m=(−1−6.5)/(4.5−0)=−5/3

The equation of the line in slope intercept form is equal to

y=mx+by=mx+b

we have

m=-5/3m=−5/3

b=6.5b=6.5 ----> the y-intercept is the point (0,6.5)

substitute

y=-(5/3)x+6.5y=−(5/3)x+6.5 ----> y=-(5/3)x+13/2y=−(5/3)x+13/2

Convert to standard form

The equation of the line in standard form is equal to

Ax+By=CAx+By=C

Where,

• A is a positive integer
• B and C are integers

Multiply by 6 to remove the fractions

6y=-2(5)x+3(13)6y=−2(5)x+3(13)

10x+6y = 3910x+6y=39 => equation of the line in standard form