Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1, 6) 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). What is the equation?

A) y = -x + 11
B) y = -x + 9
C) y = x - 5
D) y = x - 6

Answer 1

To find the equation of the line that contains the line segment CD, we need to find the slope of the line using the formula slope = (y2 - y1) / (x2 - x1). Using the coordinates of points C(8, 3) and D(x, y), we can substitute them into the formula to find the slope. Then, we can write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. Substituting the coordinates of point C into the equation allows us to find the value of b.

Step-by-step explanation:

To find the equation of the line that contains the line segment CD, we need to first find the slope of the line. The slope of a line can be found using the formula: slope = (y2 - y1) / (x2 - x1).

Using the coordinates of points C(8, 3) and D(x, y), the slope is given by: slope = (y - 3) / (x - 8).

The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Since point C(8, 3) lies on the line, we can substitute its coordinates into the equation to find b.

Substituting the coordinates of point C(8, 3) into the equation, we get: 3 = slope(8) + b. Substituting the value of slope, we have: 3 = [(y - 3) / (x - 8)](8) + b. Simplifying this equation gives us the equation of the line that contains the line segment CD.

After simplifying and rearranging the equation, we get:

y = (1/8)x - (5/8)