13.

M(6, 6) is the midpoint of . The coordinates of S are (8, 9). What are the coordinates of R?

(7, 7.5)

(2.5, 4)

(4, 3)

(10, 12)

5 answers

To find the coordinates of R, we can use the midpoint formula which states that the coordinates of the midpoint (M) between two points (S and R in this case) is the average of the x-coordinates and the average of the y-coordinates.

Given:
M(6, 6) is the midpoint of SR.
Coordinates of S are (8, 9).

Let the coordinates of point R be (x, y).

Now, using the midpoint formula:
M(x, y) = ((8 + x) / 2, (9 + y) / 2)
(6, 6) = ((8 + x) / 2, (9 + y) / 2)

Solving the equations:
6 = (8 + x) / 2
6 = (9 + y) / 2

12 = 8 + x
12 = 9 + y

x = 4
y = 3

Therefore, the coordinates of R are (4, 3) which means the correct answer is:
(4, 3)
17.

If EF = 2x – 12, FG = 3x – 15, and EG = 23, find the values of x, EF, and FG.

x = 3, EF = −6, FG = −6

x = 10, EF = 8, FG = 15

x = 10, EF = 32, FG = 45

x = 3, EF = 8, FG = 15
Given:
EF = 2x – 12
FG = 3x – 15
EG = 23

Since E is the vertex, the sum of the lengths of EF and FG is equal to the length of EG.
EF + FG = EG
2x - 12 + 3x - 15 = 23
5x - 27 = 23
5x = 50
x = 10

Now, we can substitute x = 10 back into the equations for EF and FG to find their values:
EF = 2(10) - 12 = 20 - 12 = 8
FG = 3(10) - 15 = 30 - 15 = 15

Therefore, the values of x, EF, and FG are:
x = 10, EF = 8, FG = 15

So, the correct answer is:
x = 10, EF = 8, FG = 15
18.
Find the circumference of a circle with a diameter of 6 cm. Leave your answer in terms of .

24 cm

9 cm

6 cm

12 cm
The circumference of a circle is calculated using the formula:

Circumference = π x Diameter

Given that the diameter of the circle is 6 cm, we can substitute this value into the formula:

Circumference = π x 6
Circumference = 6π

Therefore, the circumference of a circle with a diameter of 6 cm is 6π cm.

This answer can also be written in decimal as approximately 18.85 cm.

So, the correct answer is:
Circumference = 6π cm