Final answer:
Lines that are perpendicular have slopes that when multiplied together equal -1. Comparing the slopes of Line A (½) and Line C (-2), we find that they indeed multiply to -1 and are thus perpendicular to each other. The answer is B) A and C.
Step-by-step explanation:
The question asks us to determine which lines are perpendicular. Two lines are perpendicular if the product of their slopes is -1.
Line A: y = ½x + 2
Line B: y = -½x + 7
Line C: y = -2x + 4
Line D: y = ½x + 5/4
Let's examine the slopes of these lines:
Line A's slope (m) is ½.
Line B's slope (m) is -½.
Line C's slope (m) is -2.
Line D's slope (m) is ½.
To find lines that are perpendicular, we multiply the slopes of each pair to see if the result is -1:
A and B: (½) * (-½) = -1/4 (not perpendicular)
A and C: (½) * (-2) = -1 (perpendicular)
B and C: (-½) * (-2) = 1 (not perpendicular)
A and D: (½) * (½) = 1/4 (not perpendicular)
Therefore, the lines that are perpendicular are Line A and Line C.