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Questions and Answers
What is the formula to find the midpoint of a line segment?
What is the formula to find the midpoint of a line segment?
If you have two points (3, 4) and (7, 10), what is the midpoint of the line segment connecting them?
If you have two points (3, 4) and (7, 10), what is the midpoint of the line segment connecting them?
How can you calculate the slope of a line?
How can you calculate the slope of a line?
What does a slope of zero indicate about a line?
What does a slope of zero indicate about a line?
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If you have two points (5, 6) and (10, 6), what is the slope of the line passing through these points?
If you have two points (5, 6) and (10, 6), what is the slope of the line passing through these points?
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What type of line has a slope with an absolute value greater than 1?
What type of line has a slope with an absolute value greater than 1?
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In a coordinate plane, where is the origin located?
In a coordinate plane, where is the origin located?
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What are the perpendicular number lines called in a coordinate plane?
What are the perpendicular number lines called in a coordinate plane?
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What do you call the point where both axes intersect on a coordinate plane?
What do you call the point where both axes intersect on a coordinate plane?
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Study Notes
Coordinate Geometry
Coordinate geometry is a mathematical field that allows us to represent geometric figures on a coordinate plane using numerical coordinates. This plane consists of two perpendicular number lines called axes, with the horizontal axis being the x-axis and the vertical axis being the y-axis. The origin, where both axes intersect, is marked as (0, 0).
Midpoint Formula
To find the midpoint of a line segment connecting points ((x_1, y_1)) and ((x_2, y_2)), you can use the following formula:
[ \text{Midpoint} = \left(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}\right) ]
For instance, if you want to find the midpoint of a segment with (x_1 = 10), (y_1 = 6), (x_2 = 2), and (y_2 = 8), you would plug these values into the formula:
[ \text{Midpoint} = \left(\frac{10 + 2}{2}, \frac{6 + 8}{2}\right) = \left(\frac{12}{2}, \frac{14}{2}\right) = (6, 7) ]
So, the midpoint of this segment is ((6, 7)).
Slope of a Line
The slope of a line can be calculated using the following formula:
[ m = \frac{y_2 - y_1}{x_2 - x_1} ]
where ((x_1, y_1)) and ((x_2, y_2)) are any two points on the line. The slope indicates the steepness or inclination of the line and is often represented as a fraction or a decimal value. If the slope is zero, the line is horizontal; if the absolute value of the slope is 1, the line is a unit slope line parallel to the axes; and if the absolute value of the slope is greater than 1, the line gets steeper.
Distance Formula
The distance between two points ((x_1, y_1)) and ((x_2, y_2)) on the coordinate plane can be calculated using the distance formula:
[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
For example, let's find the distance between points (A(3, 5)) and (B(10, 8)):
[ d = \sqrt{(10 - 3)^2 + (8 - 5)^2} = \sqrt{49 + 9} = \sqrt{58} ]
So, the distance between point (A) and (B) is approximately 8 units.
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Description
Test your knowledge on the basics of coordinate geometry including the midpoint formula, slope calculation, and distance formula. Learn how to find midpoints, slopes, and distances between points on a coordinate plane.
