Question

| BU
I is the midpoint of BG
BI = 4y + 8
IG= 20
Find BG​

Answer 1

BG = 40 units

Step-by-step explanation:

If I is the midpoint of line BG

but BI = 4y + 8

and IG is = 20

line BG = BI + IG

= (4y + 8) + 20

= 4y + 28

but since its distance are equal

BI = IG

4Y + 8 = 20

solving for y

4y = 20-8

4y = 12

y = 3

substituting the value of in value of BG

BG = 4y + 28

BG = (4*3) + 28

BG = 12 + 28

BG = 40

Answer 2

40 units

Explanation:

The midpoint of the segment is the point on that line segment that divides the segment into two congruent segments.

If I is the midpoint of the segment BG, then segments BI and IG are congruent segments.

BI = 4y + 8 units

IG = 20 units

Hence,

`4y+8=20\\ \\4y=20-8\\ \\4y=12\\ \\y=3`

The segment additional postulate states that if we are given two points on a line segment, B and G, a third point I lies on the line segment BG if and only if the distances between the points meet the requirements of the equation

BI + IG = BG.

So,

`BG=4y+8+20=4y+28=4\cdot 3+28=12+28=40\ units`