Answer:
Part 1) The distance is
Part 2) The measure of angle 2 is 121°
Part 3) The coordinates of endpoint V are (7,-27)
Part 4) The value of x is 10
Step-by-step explanation:
Part 1) Find the distance between M(6,16) and Z(-1,14)
we know that
the formula to calculate the distance between two points is equal to
substitute the given values in the formula
Part 2) Find the measure m∠2
we know that
If two angles are supplementary, then their sum is equal to 180 degrees
In this problem we have
m∠1+m∠2=180°
substitute the given values
Solve for y
<u><em>Find the measure of m∠2</em></u>
substitute the value of y
Part 3) The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5) Find the coordinates of endpoint V
we know that
The formula to calculate the midpoint between two points is
we have
substitute and solve for (x2,y2)
so
<em>Equation 1</em>
<em>Equation 2</em>
therefore
The coordinates of endpoint V are (7,-27)
Part 4) GI bisects ∠DGH so that ∠DGI is (x-3) and ∠IGH is (2x-13) Find the value of x
we know that
If GI bisects ∠DGH
then
∠DGI=∠IGH
Remember that bisects means, divide into two equal parts
substitute the given values
solve for x