Question

A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is true?

Answer 1

R u able to find out the slope of ab n cd

Answer 2

If you tell me the formula I'm sure I could

Answer 3

Slope=(y1-y2)/(x1-x2)

Answer 4

So which points do I plug in?

Answer 5

A(x1,y1),B(x2,y2)

Answer 6

When u r going to find out the slope of AB, u will plug in the coordinates of A nd B

Answer 7

Okay so we can eliminate A

Answer 8

and C

Answer 9

I'm leaning towards B or D

Answer 10

by mere inspection using the illustration i've posted, the second option can't be true AB and CD aren't parallel. They intersect each other.

Answer 11

So D!

Answer 12

Checking for the first option.
AB and CD are perpendicular lines.
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If AB and CD are perpendicular, then it follows that the slope of the line AB is the negative reciprocal of the slope of line CD.
Let's check!
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\[m = \frac{ y_2-y_1 }{ x_2-x_1 }\]
A(-8,1) B(-2,4) C(-3,-1) D(-6,5)
AB:
\[m = \frac{ 4-1 }{ -2-(-8) }\]
\[m = \frac{ 1 }{ 2 }\]
CD:
\[m = \frac{ 5-(-1) }{ -6-(-3) }\]
\[m= -2\]
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what have you noticed of the slopes of AB and CD?

Answer 13

it's not D i can assure you if we based it on the given.

Answer 14

Well the slope of AB is 1/2 and the slope of CD is -2

Answer 15

isn't it that -2 is negative reciprocal of 1/2? therefore the lines AB and CD are perpendicular

Answer 16

Okay so B?

Answer 17

Let's check for the other options.
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As i've said earlier, you just have to look at the plotted points and you'll know 2nd option is wrong.
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Third option is surely wrong since we've got the lines AB and CD perpendicular in the previous computation.
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Let's check for the last option
If lines AC and BD are parallel, then their slopes must be identical
A(-8,1) B(-2,4) C(-3,-1) D(-6,5)
\[m = \frac{ y_2-y_1 }{ x_2-x_1 }\]
AC:
\[m = \frac{ -1-1 }{ -3-(-8) }\]
\[m = -\frac{ 2 }{ 5 }\]
BD:
\[m = \frac{ 5-4 }{ -6-(-2) }\]
\[m = -\frac{ 1 }{ 4 }\]
Their slopes are not equal therefore lines AC and BD are not parallel

Answer 18

Only the first option is true.

Answer 19

AB and CD are perpendicular lines

Answer 20

Thank you, you really helped!

Answer 21

yw :)