Question

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

Answer 1

Part 1) The distance is
`d=7.3\ units`

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

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

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the given values in the formula

`d=\sqrt{(14-16)^(2)+(-1-6)^(2)}`

`d=\sqrt{(-2)^(2)+(-7)^(2)}`

`d=√(53)\ units`

`d=7.3\ units`

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

`(4y+7)\°+(9y+4)\°= 180\°`

Solve for y

`(13y+11)\°= 180\°`

`13y= 180-11`

`13y=169`

`y=13`

Find the measure of m∠2

`(9y+4)\°`

substitute the value of y

`(9(13)+4)=121\°`

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

`M=((x1+x2)/(2),(y1+y2)/(2))`

we have

`M(5,-11)`

`(x1,y1)=(3,5)`

substitute and solve for (x2,y2)

`(5,-11)=((3+x2)/(2),(5+y2)/(2))`

so

Equation 1

`5=(3+x2)/2`

`10=3+x2`

`x2=7`

Equation 2

`-11=(5+y2)/2`

`-22=(5+y2)`

`y2=-27`

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

`x-3=2x-13`

solve for x

`2x-x=-3+13`

`x=10`