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Points A, B, and C are collinear and B lies between A and C. If AC = 48, AB = 2x + 2, and BC = 3x + 6, what is BC?
BC=


On a number line, suppose point E has a coordinate of −3,and EG=8.What are the possible coordinates of point G?
The possible coordinates for G are?
Please help!

Answers

Answer 1

The measure of side BC is 30 units.

Given:

Points A, B, and C are collinear and B lies between A and C.

[tex]AC=48[/tex]

[tex]AB=2x+2[/tex]

[tex]BC=3x+6[/tex]

To find:

The value of BC.

Solution:

Points A, B, and C are collinear and B lies between A and C. So,

[tex]AB+BC=AC[/tex]              [Segment addition postulate]

[tex](2x+2)+(3x+6)=48[/tex]

[tex]5x+8=48[/tex]

Subtract 8 from both sides.

[tex]5x=48-8[/tex]

[tex]5x=40[/tex]

Divide both sides by 5.

[tex]\dfrac{5x}{5}=\dfrac{40}{5}[/tex]

[tex]x=8[/tex]

Now,

[tex]BC=3(8)+6[/tex]

[tex]BC=24+6[/tex]

[tex]BC=30[/tex]

Therefore, the value of BC is 30.

--------------------------------------------------------------------------------------------------------------

The possible coordinates for G are -11 and 5.

Given:

On a number line, suppose point E has a coordinate of [tex]-3[/tex], and [tex]EG=8[/tex].

To find:

The possible coordinates of point G.

Solution:

Either point G lies 8 units left of point E or 8 units right of point E.

[tex]G=-3-8[/tex]

[tex]G=-11[/tex]

And

[tex]G=-3+8[/tex]

[tex]G=5[/tex]

Therefore, the possible coordinates for G are -11 and 5.

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