Question

Pls answer all the ones with blue circles

Answer 1

1. Midpoints:

(a) The midpoint of (5,11) and (3,1) is (4,6).

(b) The midpoint of (7,-5) and (3,3) is (5,-1).

2. Missing Measures:

(a) FG = 2y + 18.

(b) FG = 8x - 30.

(c) FG = 42, a = 4.71.

**1. Find the coordinates of the midpoint:**

(a) For the points (5,11) and (3,1):

`\[ \text{Midpoint} = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right) \]`

`\[ \text{Midpoint} = \left(\frac{{5 + 3}}{2}, \frac{{11 + 1}}{2}\right) = (4, 6) \]`

(b) For the points (7,-5) and (3,3):

`\[ \text{Midpoint} = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right) \]`

`\[ \text{Midpoint} = \left(\frac{{7 + 3}}{2}, \frac{{-5 + 3}}{2}\right) = (5, -1) \]`

**2. Suppose M is the midpoint of FG. Find each missing measure:**

(a) For FM = 5y + 13, MG = 5 - 3y, and FG = ?

FG = FM + MG

FG = (5y + 13) + (5 - 3y)

FG = 2y + 18

(b) For FM = 3x - 4, MG = 5x - 26, and FG = ?

FG = FM + MG

FG = (3x - 4) + (5x - 26)

FG = 8x - 30

(c) For FM = 8a + 1, FG = 42, and a = ?

FG = FM + MG

42 = (8a + 1) + (8 - a)

42 = 7a + 9

7a = 33

a = 4.71 (rounded to two decimal places)