+39 Let O be the origin. Points P and Q lie in the first quadrant. The slope of line segment OP is 1 and the slope of line segment is 3. If then compute the slope of line segment
Note: The point (x,y) lies in the first quadrant if both and are positive.
+866 Understanding the Slopes:
Slope of line segment OP = 1: This means for every 1 unit you move up on the y-axis, you also move 1 unit to the right on the x-axis.
Since O is the origin (0,0), point P will be at (x, x) for some positive value x.
Slope of line segment PQ = 3: This means for every 3 units you move up on the y-axis, you move 1 unit to the right on the x-axis.
Finding Coordinates of P:
As mentioned earlier, P lies at (x, x).
Connecting P and Q:
We know the slope of PQ is 3. We need to find the y-coordinate of point Q relative to P (i.e., how much we move up from P). Let the y-coordinate of Q be y.
Relating Coordinates using Slope:
The difference in y-coordinates (y - x) is 3 times the difference in x-coordinates (which is just x in this case).
Setting up the Equation:
y - x = 3x
Combining Like Terms:
y = 4x
Finding the Slope of PQ:
Slope of PQ = (Change in y) / (Change in x) = (y_Q - y_P) / (x_Q - x_P)
Since both P and Q lie on the positive x-axis (first quadrant), x_Q and x_P are both positive values. Therefore, we can divide both sides of the equation y = 4x by x (assuming x is not zero) to get:
y/x = 4
This gives us the slope of line segment PQ, which is 4.
