Lines
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SAT Math › Lines
Which of the following lines is perpendicular to the line 
Explanation
Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.
The slope of this line is 
Now we need to find the answer choice with this slope by converting to slope-intercept form.
This equation has a slope of 
There is a line defined by the equation below:
There is a second line that passes through the point 
Explanation
Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.
3x + 4y = 12
4y = _–_3x + 12
y = –(3/4)x + 3
slope = _–_3/4
We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.
y = mx + b
2 = _–_3/4(1) + b
2 = _–_3/4 + b
b = 2 + 3/4 = 2.75
Plug the y-intercept back into the equation to get our final answer.
y = –(3/4)x + 2.75
What line is perpendicular to 
Explanation
Convert the given equation to slope-intercept form.
The slope of this line is 
The perpendicular slope is 
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is 
Which of the following lines is perpendicular to the line
Explanation
Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.
The slope of this line is
Now we need to find the answer choice with this slope by converting to slope-intercept form.
This equation has a slope of
One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?
45'
40'
50'
35'
30'
Explanation
AB = 10 ’
BC = AC – AB = 25’ – 10’ = 15’
CD = 2 * AB = 2 * 10’ = 20 ’
AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’
One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?
45'
40'
50'
35'
30'
Explanation
AB = 10 ’
BC = AC – AB = 25’ – 10’ = 15’
CD = 2 * AB = 2 * 10’ = 20 ’
AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’
A line segment has endpoints (0,4) and (5,6). What are the coordinates of the midpoint?
(0,4)
(0,6)
(2.5,-5)
(2.5,5)
(3,9)
Explanation
A line segment has endpoints (0,4) and (5,6). To find the midpoint, use the midpoint formula:
X: (x1+x2)/2 = (0+5)/2 = 2.5
Y: (y1+y2)/2 = (4+6)/2 = 5
The coordinates of the midpoint are (2.5,5).
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
36
21
12
44
48
Explanation
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
Consider the lines described by the following two equations:
4y = 3x2
3y = 4x2
Find the vertical distance between the two lines at the points where x = 6.
36
21
12
44
48
Explanation
Since the vertical coordinates of each point are given by y, solve each equation for y and plug in 6 for x, as follows:
Taking the difference of the resulting y -values give the vertical distance between the points (6,27) and (6,48), which is 21.
A line segment has endpoints (0,4) and (5,6). What are the coordinates of the midpoint?
(0,4)
(0,6)
(2.5,-5)
(2.5,5)
(3,9)
Explanation
A line segment has endpoints (0,4) and (5,6). To find the midpoint, use the midpoint formula:
X: (x1+x2)/2 = (0+5)/2 = 2.5
Y: (y1+y2)/2 = (4+6)/2 = 5
The coordinates of the midpoint are (2.5,5).