Question

GI−→
bisects ∠DGH
so that m∠DGI
is x−3
and m∠IGH
is 2x−13
. Find the value of x.

(2 points)

Answer 1

The midpoint of UV¯¯¯¯¯
is (5,−11)
. The coordinates of one endpoint are U(3,5)
. Find the coordinates of endpoint V.

Answer 2

Find the distance between points M(6,16)
and Z(−1,14)
to the nearest tenth.

Answer 3

Since GI bisects ∠DGH, we have:

m∠DGI = m∠IGH.

From the given information, we can set up the following equation:

x - 3 = 2x - 13.

Solving for x, we can subtract x from both sides:

-3 = x - 13.

Then, we add 13 to both sides:

10 = x.

Therefore, the value of x is 10.

Answer 4

We can use the midpoint formula to find the coordinates of endpoint V.

The midpoint formula states that the coordinates of the midpoint (M) between two endpoints (P and Q) is the average of the x-coordinates and the average of the y-coordinates:

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

In this case, we know that:

M = (5, -11).
P = (3, 5).

Let V = (x, y).

Using the midpoint formula, we can set up the following equations:

5 = (3 + x)/2,

-11 = (5 + y)/2.

To solve for x:

Multiply both sides of the first equation by 2:

10 = 3 + x.

Subtract 3 from both sides:

7 = x.

So the x-coordinate of endpoint V is 7.

To solve for y:

Multiply both sides of the second equation by 2:

-22 = 5 + y.

Subtract 5 from both sides:

-27 = y.

So the y-coordinate of endpoint V is -27.

Therefore, the coordinates of endpoint V are V(7, -27).

Answer 5

To find the distance between two points (x1, y1) and (x2, y2), we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

In this case, we have:

M(6, 16) -> (x1, y1)
Z(-1, 14) -> (x2, y2)

Plugging these values into the formula, we get:

d = sqrt((-1 - 6)^2 + (14 - 16)^2).

Simplifying further:

d = sqrt((-7)^2 + (-2)^2).

Calculating:

d = sqrt(49 + 4).

d = sqrt(53).

To the nearest tenth, the distance is approximately:

d ≈ 7.3.

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.3 units.