The ratio has a total of 2+3=5 units, of which 2 correspond to the length of segment AM. The difference of x-coordinates Bx-Ax = 20-0 = 20. 2/5 of that amount is (2/5)*20 = 8, so the x-coordinate of M is
Mx = 8 + Ax = 8 + 0 = 8
The difference of y-coordinates is 0 - 15 = -15. 2/5 of that amount is (2/5)*(-15) = -6, so the y-coordinate of M is
... My = -6 + Ay = -6 + 15 = 9
The point M is (Mx, My) = (8, 9).
Answer:
B. Yes. Their slopes have product -1.
Step-by-step explanation:
Given:
Line passing through P(-3, -2) and Q(2, 3)
Line passing through R(10, -1) and S(15, -6)
Required:
To determine if both lines are perpendicular.
SOLUTION:
Two lines are considered perpendicular if the product of their slopes equal -1.
To determine if both lines given in the question are perpendicular, first, calculate their slope using:
Slope of line passing through P(-3, -2) and Q(2, 3):
Let,
Slope of line passing through R(10, -1) and S(15, -6):
Let,
The product of their slopes = 1 × -1 = -1
<u><em>Therefore, the lines are perpendicular.</em></u>
The answer is: <em><u>B. "Yes. Their slopes have product -1."</u></em>