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Reptile [31]
3 years ago
5

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(3, 5) and B(5, 1). Find the equation of the line that

contains the given segment. The line segment is CD and point C is at (7, 2
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
3 0

Answer:

2x + y = 16

Step-by-step explanation:

In rectangle side AB and side CD are parallel, so the slope of both the lines will be same it means that they are parallel to each other.

slope of line AB:

\textrm{m}=\frac{\textrm{y}_{A}-\textrm{y}_{B}}{\textrm{x}_{A}-\textrm{x}_{B}}\\\textrm{m}=\frac{5-1}{3-5}=\frac{4}{-2}=-2\\\therefore \textrm{m}=-2

slope of line CD = slope of line AB = -2

∴ equation of line CD:

\textrm{y}-\textrm{y}_{C}=\textrm{m}(\textrm{x}-\textrm{x}_{C})\\ \textrm{y}-2=-2(\textrm{x}-7)\\2\textrm{x}+\textrm{y}=16

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A line passes through the points (5, –7.5) and has a y-intercept of 10.
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need help with explanation?

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(10+-7 - -2) / (-2 - -1)
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Nice use of brackets. We know exactly what you mean.

(10 - 7 + 2) / (-2 + 1) Notice that with an even number of - signs, you get a plus and with and odd number you get a minus.

(5) / (-1) = - 5 answer

Edit

Numerator

10 does not change.

+ - 7 Here a plus and a minus are put together. There is 1 minus sign which is an odd number of minus signs so the 7 is minus

- - 2 Here there are 2 minus signs. They become plus because 2 is even, and an even number of minuses become a plus so you have +2

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