ACT Math : Coordinate Plane
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #3 : How To Find The Midpoint Of A Line Segment
What is the midpoint between 
Using the midpoint formula,
We get:
Which becomes: which becomes
Example Question #10 : How To Find The Midpoint Of A Line Segment
What is the midpoint of a line segment with endpoints 
The midpoint of a line can be found using the midpoint formula, given by:
Thus when we plug in our values we get the midpoint is
Example Question #14 : Midpoint Formula
What is the midpoint of the line with endpoints:
To find the midpoint given two points, use the formula:
Example Question #141 : Coordinate Plane
A line segment has endpoints at 
What is the midpoint of the line segment?
The midpoint can be found by using equations that calculate the values of its x- and y-coordinates. The x-coordinate can be found using the following equation:
Likewise, we will calculate the y-coordinate using another formula:
These formulas take the average of each coordinate separately in order to calculate the midpoint. In order to solve our question we will substitute in our given values and solve.
Example Question #142 : Algebra
A school superintendent is observing bus routes of students using a town map overlaid with a coordinate plane. Two students, Jon and Steve, live on the same street. Their houses correspond to the coordinates of (-3, 4) and (5,8), respectively, on the map. If there is a bus stop exactly between their two houses, what are the coordinates of the bus stop on the map?
The midpoint formula must be used to find the midpoint of the line segment joining Jon's and Steve's houses. Use the following formula to find the midpoint:
In this formula, 
In this case, the bus stop is at the following coordinate on the town map:
Example Question #1 : X And Y Intercept
Find the slope of the following line: 6x – 4y = 10
–5/2
–1.5
5/2
1.5
1.5
Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.
The slope is 1.5.
Example Question #141 : Coordinate Plane
What is the x-intercept of the line in the standard 
3
12
-24
2
2
This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.
Add 2 to both sides of the equation.
Divide both sides of the equation by 6.
The line crosses the x-axis at 2.
Example Question #142 : Coordinate Plane
What is the equation of a line that has an x-intercept of 4 and a y-intercept of -6?
The equation of a line can be written in the following form:
In this formula, m is the slope, and b represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:
We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values. It is formally written as the following equation:
The problem provides the two intercepts of the line, which can be written as 
Substitute the calculated values into the general equation of a line to get the correct answer:
Example Question #142 : Coordinate Plane
What are the y and x intercepts of the given equation, respectively?
y = 2x – 2
(0, –2), (–2, 0)
(0, –2), (2, 0)
(0, 2), (2, 0)
(0, –2), (1, 0)
(0, 0), (0, 0)
(0, –2), (1, 0)
The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)
Example Question #1 : X And Y Intercept
What is the x-intercept of the following line?
y = –3x + 12
–4
4
1/4
2
–1/4
4
The x-intercept occurs when the y-coordinate = 0.
y = –3x + 12
0 = –3x + 12
3x = 12
x = 12/3 = 4
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