A is a definite pick, because we can simply extend a line from P in the direction given by the slope, and find Q when it intersects x=25. At that point we can determine whether t > -18.
B shows only the distance from P, which could intersect the line x=25 in two places (positive and negative slope). Because that line is 8 units to the right from P, a distance of 10 would be the hypoteneuse of a right triangle, and the second leg would be 6. -20 +/- 6 won't provide enough information to determine whether t > -18.
C. Knowing that Q is the midpoint of line PR, we know that its y-component t is half of (3t+34) - (-20) (the vertical distance between P and R). So t = 1/2(3t+54), which we don't have to actually solve, but we know we can because we have one equation and one unknown, and that would allow us to determine whether t > -18.
The answer is A and C.
Carcass wrote:
Both of the points P( 17, − 20) and Q( 25, t) are in the xy-plane. Which of the following statements alone give( s) sufficient additional information to determine whether \(t > − 18\) such sets of integers.?
Indicate all such statements.
A. The slope of the line that goes through the points P( 17, − 20) and Q( 25, t) is 3/4
B. The distance between the points P( 17, − 20) and Q( 25, t) is 10.
C. The point Q( 25, t) is the midpoint of the line segment whose endpoints are P( 17, − 20) and R( 33, 3t + 34).