Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A (2, 7) and B (5, 1). Find the equation of the line that contains the given segment. he line segment is AD .

Answer 1

To determine the equation of line AD, we calculate the slope using points A and B, then use the slope and point A to write the equation. The final equation of line AD is y = -2x + 11.

Step-by-step explanation:

To find the equation of the line that contains segment AD, we must first understand that segment AB is not the side AD of the rectangle, but we can use the given information about segment AB to find the slope of line AD since rectangles have parallel opposite sides. We can assume that AB is parallel to CD, and therefore, the slopes of AB and AD will be the same.

The slope (m) of a line containing two points (x1, y1) and (x2, y2) is calculated as:

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

Using points A (2, 7) and B (5, 1):

m = (1 - 7) / (5 - 2) = -6 / 3 = -2

The slope of line AD will also be -2 since it is parallel to line AB. Next, using point A and the slope, we can find the equation of line AD by plugging them into the point-slope form equation, y - y1 = m(x - x1).

y - 7 = -2(x - 2), which simplifies to:

y - 7 = -2x + 4

y = -2x + 11

The equation of line AD is y = -2x + 11.

Answer 2

Equation of the line thru 2 points:y-y₁=((y₂-y₁)/(x₂-x₁))*(x-x₁)

A(x₁,y₁)=(2,7). B(x₂,y₂)=(5,1)
y-7=((1-7)/(5-2))*(x-2)
y-7=-2*(x-2)
y-7=-2x+4
y=-2x+11