Respuesta :
The obtained answers for the given line segments are as follows:
9. The value of the line segment [tex]\overline {DE}[/tex] = 43; Where [tex]\overline { DF}[/tex] = 61 and [tex]\overline {EF}[/tex]
10. The value of x is 6; Where [tex]\overline {DE}[/tex] = 4x - 1, [tex]\overline {EF}[/tex] = 9, and [tex]\overline { DF}[/tex] = 9x - 22
11. The value of line segment [tex]\overline {EF}[/tex] = 32; Where [tex]\overline { DF}[/tex] = 78, [tex]\overline {DE}[/tex] = 5x - 9, and [tex]\overline {EF}[/tex] = 2x + 10
12. The value of line segment [tex]\overline { DF}[/tex] = 57; Where [tex]\overline {DE}[/tex] = 4x + 10 [tex]\overline {EF}[/tex] = 2x - 1, and [tex]\overline { DF}[/tex] = 9x - 15.
What is a line segment?
- A line segment is a part of a line formed by infinite points with two endpoints at both ends.
- The line segment is represented by the two endpoints.
- A line segment has a finite length.
Calculation:
The calculation for the required values is as follows:
9. Finding [tex]\overline{DE}[/tex]:
It is given that,
[tex]\overline{DF}[/tex] = 61; [tex]\overline{EF}[/tex] = 18
From the figure, we can write
[tex]\overline{DF} = \overline{DE} + \overline{EF}[/tex]
On substituting the given values,
61 = [tex]\overline{DE}[/tex] + 18
⇒ [tex]\overline{DE}[/tex] = 61 - 18
∴ [tex]\overline{DE}[/tex] = 43
10. Finding x:
It is given that,
[tex]\overline {DE}[/tex] = 4x - 1, [tex]\overline {EF}[/tex] = 9, and [tex]\overline { DF}[/tex] = 9x - 22
From the figure we have
[tex]\overline{DF} = \overline{DE} + \overline{EF}[/tex]
On substituting,
(9x - 22) = (4x - 1) + 9
⇒ 9x - 22 = 4x - 1 + 9
⇒ 9x - 4x = 8 + 22
⇒ 5x = 30
∴ x = 6
11. Finding [tex]\overline{EF}[/tex]:
It is given that,
[tex]\overline { DF}[/tex] = 78, [tex]\overline {DE}[/tex] = 5x - 9, and [tex]\overline {EF}[/tex] = 2x + 10
From the figure we have
[tex]\overline{DF} = \overline{DE} + \overline{EF}[/tex]
On substituting,
78 = (5x - 9) + (2x + 10)
⇒ 78 = 5x - 9 + 2x + 10
⇒ 7x + 1 = 78
⇒ 7x = 78 - 1
⇒ 7x = 77
∴ x = 11
On substituting x = 11 in [tex]\overline {EF}[/tex] = 2x + 10; we get
[tex]\overline {EF}[/tex] = 2(11) + 10
= 22 + 10
= 32
Therefore, the value of the line segment [tex]\overline {EF}[/tex] is 32.
12. Finding [tex]\overline {DF}[/tex]:
It is given that,
[tex]\overline {DE}[/tex] = 4x + 10 [tex]\overline {EF}[/tex] = 2x - 1, and [tex]\overline { DF}[/tex] = 9x - 15
From the figure we have
[tex]\overline{DF} = \overline{DE} + \overline{EF}[/tex]
On substituting,
(9x - 15) = (4x + 10) + (2x - 1)
⇒ 9x - 15 = 4x + 10 + 2x - 1
⇒ 9x - 15 = 6x + 9
⇒ 9x - 6x = 9 + 15
⇒ 3x = 24
∴ x = 8
On substituting x = 8 in [tex]\overline { DF}[/tex] = 9x - 15; we get
[tex]\overline { DF}[/tex] = 9(8) - 15
= 72 - 15
= 57
Therefore, the value of the line segment [tex]\overline { DF}[/tex] is 57.
Learn more about line segments here:
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