Indicate the equation of the given line in standard form. show all of your work for full credit.
the line containing the median of the trapezoid whose vertices are r(-1,5), s(1,8), t(7,-2), and u(2,0)

Step-by-step 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

we have

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

substitute the values

step 3

Find the midpoint TU

The midpoint of segment RS is equal to the formula

we have

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

substitute the values

step 4

Find the equation of the line containing the median

we have the points

Find the slope m

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

we have

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

substitute

---->

Convert to standard form

The equation of the line in standard form is equal to

where

A is a positive integer

B and C are integers

Multiply by 6 to remove the fractions

----> equation of the line in standard form

answer: asdfghjkl,mnbv

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²