SAT数学Problem Solving练习题(16)
- 2017年07月25日14:18 来源:互联网
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Question 16: In the x,y plane, which of the following statements are true?
I. Line y + x = 5 is perpendicular to line y - x = 5.
II. Lines y + x = 5 and y - x = 5 intersect each other on the y axis.
III. Lines y + x = 5 and y - x = 5 intersect each other on the x axis.
(a) I and III are both true.
(b) I is the only true statement.
(c) II is the only true statement.
(d) I and II are both true.
Answer: y + x = 5 can be written as y = -x + 5. The slope of this equation is m1 = -1.
y - x = 5 can be written as y = x + 5. The slope of this equation is m2 = 1.
m2 = -1/m1 so the 2 lines are perpendicular.
We also need to find where the 2 lines intersect. If we add the 2 equations, 2·y = 10, y = 5.
From the first equation, x = 5 - y = 5 - 5 = 0. In conclusion the lines intersect at (0, 5) and this point is on the y axis.
In conclusion I and II statements are correct.