Answer:
P = 7/3 and q = 0
Step-by-step explanation:
The given parameters are;
The endpoints of the segment are, (3, -4) and (1, 2)
The points that trisect the given points are P and Q with coordinates (p, -2) and (5/3, q) respectively
Therefore, we have;
The first point of the trisection cuts 1/3 of the length from one point and the second point of the trisection cuts 2/3 of the length from the same point
The coordinates of P or Q = (3 - (3 - 1)/3, -4 - (-4 - 2)/3) = (7/3 , -2)
Therefore, given that the y-coordinate value of the derived point coincides with the y-coordinate value of the point P, (p, -2) and there is only one point with x = -2 on the line, we have that the coordinate of the point P is (p, -2) = (7/3 , -2)
∴ P = 7/3
Similarly we have the second point of the trisection, Q, given as follows;
We are already given the x-coordinate value of the point Q as the 5/3 in (5/3, q)
Point Q = (5/3, q) = (3 - 2×(3 - 1)/3, -4 - 2×(-4 - 2)/3) = (5/3 , 0)
Point Q = (5/3, q) = (5/3 , 0)
∴ q = 0.
bh</h3><h3 /><h3>The area of the triangle above the x-axis:</h3><h3>2 x 3 = 6</h3><h3>6 ÷ 2 = <u>3</u></h3><h3 /><h3>The area of the triangle below the x-axis:</h3><h3>2 x 6 = 12</h3><h3>12 ÷ 2 = <u>6</u></h3><h3 /><h2>3 + 6 = 9</h2><h3 /><h3><em>Please let me know if I am wrong.</em></h3>