BTGModeratorVI wrote: ↑Mon Jun 22, 2020 6:17 am
In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k ?
A. (9, 4)
B. (4, 9)
C. (–4, 6)
D. (–6, –9)
E. (–6, –4)
Answer:
E
Source: Official guide
Solution:
Since line k passes through points (0, 0) and (3, 2), its slope is (2 - 0) / (3 - 0) = 2/3. If a point is on line k, then the slope calculated using its coordinates and one of the given points should be 2/3, the slope of the line. Since (0, 0) is an “easier” point for calculations than (3, 2), we will use (0, 0). For choice A, the slope between (0, 0) and (9, 4) is (4 - 0) / (9 - 0) = 4/9. We see that this is not 2/3, so choice A is not the correct answer.
Notice that the slope between (0, 0) and (a, b) is b/a. Therefore, we can determine the slope of the line easily for the other four choices and determine which is on line k.
B. (4, 9) → slope = 9/4 ≠ 2/3
C. (-4, 6) → slope = 6/(-4) = -3/2 ≠ 2/3
D. (-6, -9) → slope = (-9)/(-6) = 3/2 ≠ 2/3
E. (-6, -4) → slope = (-4)/(-6) = 2/3
Answer: E
