Answer:
Part 1) The distance is [tex]d=7.3\ units[/tex]
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
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the given values in the formula
[tex]d=\sqrt{(14-16)^{2}+(-1-6)^{2}}[/tex]
[tex]d=\sqrt{(-2)^{2}+(-7)^{2}}[/tex]
[tex]d=\sqrt{53}\ units[/tex]
[tex]d=7.3\ units[/tex]
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
[tex](4y+7)\°+(9y+4)\°= 180\°[/tex]
Solve for y
[tex](13y+11)\°= 180\°[/tex]
[tex]13y= 180-11[/tex]
[tex]13y=169[/tex]
[tex]y=13[/tex]
Find the measure of m∠2
[tex](9y+4)\°[/tex]
substitute the value of y
[tex](9(13)+4)=121\°[/tex]
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
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
[tex]M(5,-11)[/tex]
[tex](x1,y1)=(3,5)[/tex]
substitute and solve for (x2,y2)
[tex](5,-11)=(\frac{3+x2}{2},\frac{5+y2}{2})[/tex]
so
Equation 1
[tex]5=(3+x2)/2[/tex]
[tex]10=3+x2[/tex]
[tex]x2=7[/tex]
Equation 2
[tex]-11=(5+y2)/2[/tex]
[tex]-22=(5+y2)[/tex]
[tex]y2=-27[/tex]
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
[tex]x-3=2x-13[/tex]
solve for x
[tex]2x-x=-3+13[/tex]
[tex]x=10[/tex]
