问答题
These exercises are designed to help you apply the mathematics concepts just covered. They are not in GRE format, but should help you to identify your areas of strength and weakness.
These exercises are designed to help you apply the mathematics concepts just covered. They are not in GRE format, but should help you to identify your areas of strength and weakness.
Coordinate Geometry
These questions will test your knowledge of operations involving the equation and the slope of a line and distance and midpoint formulas.
Answer the following questions.
These questions will test your knowledge of operations involving the equation and the slope of a line and distance and midpoint formulas.
Answer the following questions.
问答题
| What is the y-intercept of the line with the equation 2y=4x+6? |
【正确答案】
【答案解析】First, rearrange the equation into the slope-intercept form by isolating y on the left side; divide both sides by 2:
y=2x+3
You know that in the slope intercept formula, y=mx+b, b is the y-intercept. Because b=3, the correct answer is 3.
问答题
| What is the slope of the line with the equation 3y=-2x+5? |
【正确答案】
【答案解析】Rearrange the equation into the slope intercept form by isolating y on the left side; divide both sides by 3:
You know that in the slope intercept formula, y=mx+b, m is the slope. Because 
the correct answer is 
You know that in the slope intercept formula, y=mx+b, m is the slope. Because the correct answer is
问答题
| What is the slope of the line x=4? |
【正确答案】
【答案解析】This equation represents a vertical line; the y-intercept is 0, so the line is parallel to the y-axis. A vertical line has an undefined slope, because the denominator is 0.
问答题
| What is the equation of a line parallel to y=4x-12 that crosses the y-axis at 3? |
【正确答案】
【答案解析】For two lines to be parallel, their slopes must be equal; therefore, in the standard equation y=mx+b, m=4. You are given that the line crosses the y-axis at 3, so the y-intercept (b) must be 3. If you substitute 4 for m and 3 for b in the standard equation, you get y=4x+3.
问答题
| What is the equation of a line perpendicular to 3x=2-y with the y-intercept 8? |
【正确答案】
【答案解析】First, rearrange the equation into slope-intercept form, by subtracting 3x and-y from both sides:
y=-3x+2
For two lines to be perpendicular, their slopes must be negative reciprocals. The negative reciprocal of-3 is . The problem also states that the perpendicular line has a y-intercept of 8. If you substitute 
for m and 8 for b in the standard equation, you get 
. The problem also states that the perpendicular line has a y-intercept of 8. If you substitute for m and 8 for b in the standard equation, you get
问答题
| What is the distance between the points (3,-4) and (9,4)? |
【正确答案】
【答案解析】Use the Distance Formula to solve this problem. Substitute the given values of x and y into the formula to solve for the distance, as follows:
问答题
| Solve for y if the distance between the two points (2,8) and (-6,y) is 17. |
【正确答案】
【答案解析】Use the Distance Formula to solve this problem. Because you are given the
distance between the points, your equation will look like this:
问答题
| What is the midpoint between (12,5) and (10, -7)? |
【正确答案】
【答案解析】Use the midpoint equation to solve this problem. First solve for the
x-coordinate, which is half the distance between 12 and 10:
Do the same for mm, which is half the distance between 5 and -7:
Therefore, the midpoint is (11,-1).
Do the same for mm, which is half the distance between 5 and -7:
Therefore, the midpoint is (11,-1).
问答题
| Solve for x if the midpoint between the two points (x,1) and (-2, -3) is (5,-1). |
【正确答案】
【答案解析】You only have to solve for the x-coordinate because you are given the y-coordinate:
问答题
| What is the distance between the points (0,5) and (5,0)? |
【正确答案】
【答案解析】Use the Distance Formula to solve this problem. Substitute the given values of x and y into the formula to solve for the distance, as follows: