All SAT Math Resources
Example Questions
Example Question #81 :有限公司ordinate Geometry
Which of the following lines is perpindicular to
None of the other answers
When determining if a two lines are perpindicular, we are only concerned about their slopes. Consider the basic equation of a line,, where m is the slope of the line. Two lines are perpindicular to each other if one slope is the negative and reciprocal of the other.
The first step of this problem is to get it into the form,, which is。Now we know that the slope, m, is。The reciprocal of that is, and the negative of that is。Therefore, any line that has a slope ofwill be perpindicular to the original line.
Example Question #82 :有限公司ordinate Geometry
Which of the following equations represents a line that is perpendicular to the line with pointsand?
If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line.
Because we know that our given line's slope is, the slope of the line perpendicular to it must be。
Example Question #83 :有限公司ordinate Geometry
Which of the following lines is NOT perpendicular to?
Perpendicular lines have slopes that are negative reciprocals. The given equation has a slope of; therefore, any lime that is perpendicular to it will have a slope of。
Example Question #84 :有限公司ordinate Geometry
Lineis given by。
Which of the following is perpendicular to?
Putting the equation of the line into slope-intercept form, we get
The slope of line, therefore, is。
In order for a line to be perpendicular to the given line, it must have a slope that is the negative reciprocal of line g's slope.
The slope of any given line perpendicular to line g must bewhen written in slope-intercept form. In other words, the equation of the perpendicular line must bewhere k is any constant.
Written in standard form, the equation of this perpendicular line must be
Therefore, the most appropriate answer is
Example Question #85 :有限公司ordinate Geometry
Given: Lines A, B, and C on the coordinate plane, as follows:
The equation of Line A is。
The equation of Line B is。
The equation of Line is。
Which of the following is a true statement?
No two of Line A, Line B, and Line C are perpendicular to each other.
Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.
Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.
None of the statements in the other choices is true.
Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.
No two of Line A, Line B, and Line C are perpendicular to each other.
Two lines are perpendicular if and only if the product of their slopes is。因此,我们需要找到所有刺的斜坡ee lines.Rewrite the equation for each line in its slope-intercept form, whereis the slope of the line.
Line A:
is already in this form. The slope of Line A is the coefficient of, which is 3.
Line B:
Isolateby working the same operations on both sides:
The slope of Line B is the coefficient of, which is 3.
Line C:
The slope of Line C is the coefficient of, which is 3.
All three lines have slope 3, so the product of the slopes of any two of the lines is。Therefore, no two of the lines are perpendicular.
Example Question #86 :有限公司ordinate Geometry
Given: Lines A, B, and C on the coordinate plane, as follows:
The equation of Line A is。
The equation of Line B is。
The equation of Line C is。
Which of the following is a true statement?
Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.
Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.
None of the statements in the other choices is true.
Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.
No two of Line A, Line B, and Line C are perpendicular to each other.
Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.
Two lines are perpendicular if and only if the product of their slopes is。因此,我们需要找到所有刺的斜坡ee lines.
Rewrite the equation for each line in its slope-intercept form, whereis the slope of the line.
Line A:
Isolateby working the same operations on both sides:
The slope of Line A is the coefficient of, which is。
Take the same steps with the equations of the other two lines:
Line B:
The slope of Line B is
Line C:
The slope of Line C is。
The product of the slopes of Lines A and B is, so these two lines are perpendicular.
The product of the slopes of Lines A and C is, so these two lines are not perpendicular.
The product of the slopes of Lines B and C is, so these two lines are not perpendicular.
Example Question #87 :有限公司ordinate Geometry
Given: Lines A, B, and C on the coordinate plane, as follows:
Line A has interceptsand。
Line B has interceptsand。
Line C has interceptsand。
Which of the following statements is true?
Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.
Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.
None of the statements in the other choices is true.
Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.
No two of Line A, Line B, and Line C are perpendicular to each other.
No two of Line A, Line B, and Line C are perpendicular to each other.
The slope of each line, given the coordinates of two points through which they pass, can be calculated by substituting the point coordinates into the slope formula
。
Line A:
Settingand substituting:
Line B:
Settingand substituting:
Line C:
Settingand substituting:
The product of the slopes of Line A and Line B is, as is the product of the slopes of Line C and Line B; Since neither product is equal to, neither pair of lines is perpendicular. Also, the slopes of Line A and Line C are equal, so the lines are parallel, not perpendicular.
Example Question #88 :有限公司ordinate Geometry
Which of the following lines is perpendicular to
The line which is perpendicular has a slope which is the negative inverse of the slope of the original line.
Example Question #89 :有限公司ordinate Geometry
Lines P and Q are parallel. Find the value of。
Since these are complementary angles, we can set up the following equation.
Now we will use the quadratic formula to solve for。
但是请注意,一个角的测量不能be negative, sois not a viable answer. The correct answer, then, is
Example Question #90 :有限公司ordinate Geometry
In thexy-plane, linelis given by the equation 2x- 3y= 5. If linelpasses through the point (a,1), what is the value ofa?
The equation of linelrelatesx-values andy-values that lie along the line. The question is asking for thex-value of a point on the line whosey-value is 1, so we are looking for thex-value on the line when they-value is 1. In the equation of the line, plug 1 in foryand solve forx:
2x- 3(1) = 5
2x- 3 = 5
2x= 8
x= 4. So the missing x-value on linelis 4.