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The endpoints of a side of rectangle ABCD in the coordinate plane are at A(2, 5) and B(6, 1). Find the equation of the line that contains the given segment.

The line segment is CD, and point C is at (8, 3).

A) y = -1/2x + 7
B) y = -1/2x + 2
C) y = 2x + 5
D) y = -2x + 17

User Orysia
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1 Answer

3 votes

Final answer:

The equation of the line containing segment CD is y = x - 5 .

The correct option is not given.

Step-by-step explanation:

To find the equation of the line containing line segment CD, you can use the slope-intercept form of the equation: y = mx + b, where m is the slope and (b) is the y-intercept.

1. **Find the slope (m):**

The slope (m) of a line passing through two points (x_1, y_1) and (x_2, y_2) is given by:

m = {y_2 - y_1} / {x_2 - x_1}

Using points C(8, 3) and D(6, 1):

m = {1 - 3} / {6 - 8} = {-2} / {-2} = 1

2. **Find the y-intercept (b):**

Using the slope-intercept form \(y = mx + b\), you can substitute one of the points. Let's use point C(8, 3):

3 = 1 . 8 + b

b = 3 - 8 = -5

So, the equation of the line CD is y = x - 5.

Comparing this with the given options:

y = x - 5

None of the provided options match exactly. There may be a typographical error or a misinterpretation in the options. Please double-check the options or the calculation steps. If there is additional information or clarification needed, feel free to provide it.

The correct option is not given.

User Nanestev
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7.3k points