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HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)

HELP HELP HELPPPP PLEASEEE Directions Determine If Segments AB And CD Are Parallel Perpendicular Or Neither AB Formed By 2 13 And 0 3 CD Formed By 5 0 And 10 3 class=

Sagot :

Given:

AB formed by (-2,13) and (0,3).

CD formed by (-5,0) and (10,3).

To find:

Whether the segments AB and CD are parallel, perpendicular, or neither.

Solution:

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

AB formed by (-2,13) and (0,3). So, the slope of AB is:

[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]

[tex]m_1=\dfrac{-10}{2}[/tex]

[tex]m_1=-5[/tex]

CD formed by (-5,0) and (10,3). So, slope of CD is:

[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]

[tex]m_2=\dfrac{3}{10+5}[/tex]

[tex]m_2=\dfrac{3}{15}[/tex]

[tex]m_2=\dfrac{1}{5}[/tex]

Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.

[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]

[tex]m_1\times m_2=-1[/tex]

Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.

Hence, the segments AB and CD are perpendicular.

Numenius

Answer:

AB is perpendicular to CD.

Step-by-step explanation:

AB formed by (-2, 13) and (0, 3)

CD formed by (-5, 0) and (10, 3)

Slope of a line passing through two points is

[tex]m= \frac{y''-y'}{x''- x'}[/tex]

The slope of line AB is

[tex]m= \frac{3- 13}{0+2} = -5[/tex]

The slope of line CD is

[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]

As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.

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