A line segment has one endpoint, A(4,7), and a slope of -5/3. Find the coordinates of another possible endpoint, B.
To find the coordinates of the other endpoint, B, we can use the given information of the slope and the coordinates of one endpoint, A.
The slope, given by m, is the rate of change between the two points on the line segment. It is calculated as:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Now, let's substitute the given information into the slope equation:
-5/3 = (y2 - 7) / (x2 - 4).
To simplify the equation, we can multiply both sides by (x2 - 4) to eliminate the fraction:
-5(x2 - 4) = 3(y2 - 7).
Expanding and rearranging the equation:
-5x2 + 20 = 3y2 - 21.
Now, we need to isolate y2 to solve for the y-coordinate of point B. Let's rearrange the equation:
3y2 = -5x2 + 41.
Dividing by 3:
y2 = (-5/3)x2 + 41/3.
This equation provides the relationship between the x-coordinate, x2, and the y-coordinate, y2, of the other endpoint, B.
To find the coordinates of B, we can choose any suitable value for x2 and substitute it into the equation to solve for y2.
For example, let's take x2 = 0:
y2 = (-5/3)(0) + 41/3,
y2 = 41/3.
So, one possible endpoint of the line segment is B(0, 41/3).
Note: You can choose any other value for x2 to find different coordinates for B.