I need help with these four questions please (68 points)

Accepted Solution

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 10Step-by-step explanation:Part 1) Find the distance between M(6,16) and Z(-1,14)we know thatthe 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∠2we know thatIf two angles are supplementary, then their sum is equal to 180 degreesIn this problem we havem∠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 thatThe 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]soEquation 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]thereforeThe 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 xwe know thatIf GI bisects ∠DGHthen ∠DGI=∠IGHRemember that bisects means, divide into two equal partssubstitute the given values[tex]x-3=2x-13[/tex]solve for x[tex]2x-x=-3+13[/tex][tex]x=10[/tex]