segment - part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

A line segment has the endpoints S(10, 7) and T(2, 7). Find the coordinates of its midpoint M.

A line segment has the endpoints S(10, 7) and T(2, 7). Find the coordinates of its midpoint M.
[URL='https://www.mathcelebrity.com/slope.php?xone=2&yone=7&slope=+&xtwo=10&ytwo=7&bvalue=+&pl=You+entered+2+points']Using our midpoint calculator[/URL], we get:
M = [B](6, 7)[/B]

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line s

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains?
This means the leftover segment has a length of:
[B]26 - x[/B]

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the othe

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the other endpoint?
The other endpoint is (8,1) using our [URL='http://www.mathcelebrity.com/mptnline.php?ept1=2&empt=5&ept2=&pl=Calculate+missing+Number+Line+item']midpoint calculator.[/URL]

B is the midpoint of AC and BC=5

B is the midpoint of AC and BC=5
Since the midpoint divides a segment into two equal segments, we know that:
AB = BC
So AB =[B] 5[/B]
And AC = 5 + 5 = [B]10[/B]

Cevian Triangle Relations

Free Cevian Triangle Relations Calculator - Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Geometric Mean of a Triangle

Free Geometric Mean of a Triangle Calculator - Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

Given: BC = EF AC = EG AB = 10 BC = 3 Prove FG = 10

Given: BC = EF
AC = EG
AB = 10
BC = 3
Prove FG = 10
[LIST]
[*]AC = AB + BC (Segment Addition Postulate)
[*]AB = 10, BC = 3 (Given)
[*]AC = 10 + 3 (Substitution Property of Equality)
[*]AC = 13 (Simplify)
[*]AC = EG, BC = EF (Given)
[*]EG = 13, EF = 3 (Segment Equivalence)
[*]EG = EF + FG (Segment Addition Postulate)
[*]13 = 3 + FG (Substitution Property of Equality)
[*]FG = 10 (Subtraction Property)
[/LIST]

Golden Ratio

Free Golden Ratio Calculator - Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

If Ef = 3x,Fg = 2x,and EG = 5

If Ef = 3x,Fg = 2x,and EG = 5
By segment addition, we have:
EF + FG = EG
3x + 2x = 5
To solve for x, we t[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B2x%3D5&pl=Solve']ype this equation into our math engine [/URL]and we get:
x = 1
So EF = 3(1) = [B]3[/B]
FG = 2(1) = [B]2[/B]

If EF = 7x , FG = 3x , and EG = 10 , what is EF?

If EF = 7x , FG = 3x , and EG = 10 , what is EF?
By segment addition:
EF + FG = EG
7x + 3x = 10
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=7x%2B3x%3D10&pl=Solve']type it in our search engine[/URL] and we get:
x = 1
Evaluating EF = 7x with x = 1, we get:
EF = 7 * 1
EF = [B]7[/B]

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?
By segment addition, we know that:
EF + FG = EG
Substituting in our values for the 3 segments, we get:
9x - 17 + 17x - 14 = 20x + 17
Group like terms and simplify:
(9 + 17)x + (-17 - 14) = 20x - 17
26x - 31 = 20x - 17
Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides
26x - 31 - 20x = 20x - 17 - 20x
[SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE]
6x - 31 = -17
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -31 and -17. To do that, we add 31 to both sides
6x - 31 + 31 = -17 + 31
[SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE]
6x = 14
[SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE]
6x/6 = 14/6
x = [B]2.3333333333333[/B]

If FG = 9, GH = 4x, and FH = 7x, what is GH?

If FG = 9, GH = 4x, and FH = 7x, what is GH?
By segment addition, we have:
FG + GH = FH
Substituting in the values given, we have:
9 + 4x = 7x
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4x%3D7x&pl=Solve']type it in our math engine[/URL] and we get:
x = 3
The question asks for GH, so with x = 3, we have:
GH = 4(3)
GH = [B]12[/B]

If FG=11, GH=x-2, and FH=3x-11, what is FH

If FG=11, GH=x-2, and FH=3x-11, what is FH
By segment addition, we have:
FG + GH = FH
11 + x - 2 = 3x - 11
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=11%2Bx-2%3D3x-11&pl=Solve']type it in or math engine[/URL] and we get:
x = 10
FH = 3x - 11. So we substitute x = 10 into this:
FH = 3(10) - 11
FH = 30 - 11
FH = [B]19[/B]

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?
From the segment addition rule, we have:
QR + RS = QS
Plugging our values in for each of these segments, we get:
16 + 4x - 17 = x + 20
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2B4x-17%3Dx%2B20&pl=Solve']we type it in our search engine[/URL] and we get:
x = 7
Take x = 7 and substitute it into RS:
RS = 4x - 17
RS = 4(7) - 17
RS = 28 - 17
RS = [B]11[/B]

KL=4, and JK=9 Find JL

KL=4, and JK=9 Find JL
Using segment addition, we know that:
JL = JK + KL
JL = 9 + 4
JL = [B]13[/B]

M is the midpoint of AB. Prove AB=2AM

M is the midpoint of AB. Prove AB=2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.
Collinear means on the same line.
By segment subtraction, we have:
AB = AC - BC
AB = 15 - 7
AB = [B]8[/B]

PQ=3.7 and PR=14.1 what is QR

PQ=3.7 and PR=14.1 what is QR
QR = PR - PQ by segment addition
QR = 14.1 - 3.7
QR = [B]10.4[/B]

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]

What is a Perpendicular Bisector

Free What is a Perpendicular Bisector Calculator - This lesson walks you through what a perpendicular bisector is and the various properties of the segment it bisects and the angles formed by the bisection

What is a Segment

Free What is a Segment Calculator - This lesson walks you through what a segment is and the various implications of a segment in geometry including the midpoint of a segment.