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One line segment had endpoints
A(-4,-6) and
B(12,6). Another line segment has endpoints
C(2,9) and
a) Determine the length of
AB.
b) Determine the midpoint of
CD.
c) Determine if
AB is perpendicular to
CD.
d) Determine the coordinates of the interse of
AB and
CD.

$1$ . One line segment had endpoints $A(-4,-6)$ and $B(12,6)$ . Another line segment has endpoints $C(2,9)$ and $\newline$ a) Determine the length of $A B$ . $\newline$ b) Determine the midpoint of $C D$ . $\newline$ c) Determine if $A B$ is perpendicular to $C D$ . $\newline$ d) Determine the coordinates of the interse of $A B$ and $C D$ .

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Write a linear equation from two points

Full solution

Q.

1

. One line segment had endpoints

A(-4,-6)

and

B(12,6)

. Another line segment has endpoints

C(2,9)

and

\newline

a) Determine the length of

A B

.

\newline

b) Determine the midpoint of

C D

.

\newline

c) Determine if

A B

is perpendicular to

C D

.

\newline

d) Determine the coordinates of the interse of

A B

and

C D

.

Find Length of AB: To find the length of AB, we use the distance formula: $\newline$ $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ . $\newline$ For points A( $-4$ , $-6$ ) and B( $12$ , $6$ ), we have: $\newline$ $d_{AB} = \sqrt{(12 - (-4))^2 + (6 - (-6))^2}$ $\newline$ $d_{AB} = \sqrt{(12 + 4)^2 + (6 + 6)^2}$ $\newline$ $d_{AB} = \sqrt{16^2 + 12^2}$ $\newline$ $d_{AB} = \sqrt{256 + 144}$ $\newline$ $d_{AB} = \sqrt{400}$ $\newline$ $d_{AB} = 20$ $\newline$ The length of AB is $20$ units.
Find Midpoint of CD: To find the midpoint of CD, we use the midpoint formula: $\newline$ M = (( $x_1 + x_2$ )/ $2$ , ( $y_1 + y_2$ )/ $2$ ). $\newline$ For points C( $2$ , $9$ ) and D(unknown), we cannot determine the midpoint because the coordinates of point D are not given. Therefore, we cannot complete this step.

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