What is the midpoint of a line segment with the endpoints (8,-3) and (-5, -9)?
A. (-6, 1.5)
B. (1.5, -6)
C. (2.5,-7)
D. (-7, 2.5)
Answer (2)
The midpoint formula is used to find the point exactly in the middle of a line segment.
The formula is: Midpoint = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) .
Substitute the given coordinates (8, -3) and (-5, -9) into the formula.
Calculate the midpoint: ( 2 8 + ( − 5 ) , 2 − 3 + ( − 9 ) ) = ( 1.5 , − 6 ) .
Explanation
Understanding the Midpoint Formula We are given the endpoints of a line segment as (8, -3) and (-5, -9). We want to find the midpoint of this line segment. The midpoint formula is given by:
Midpoint = ( 2 x 1 + x 2 , 2 y 1 + y 2 )
where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the coordinates of the endpoints.
Applying the Formula Let's plug in the given coordinates into the midpoint formula:
( x 1 , y 1 ) = ( 8 , − 3 ) ( x 2 , y 2 ) = ( − 5 , − 9 )
So, the midpoint is:
Midpoint = ( 2 8 + ( − 5 ) , 2 − 3 + ( − 9 ) )
Calculating the Midpoint Now, let's calculate the coordinates of the midpoint:
Midpoint = ( 2 8 − 5 , 2 − 3 − 9 ) Midpoint = ( 2 3 , 2 − 12 ) Midpoint = ( 1.5 , − 6 )
Final Answer Therefore, the midpoint of the line segment with endpoints (8, -3) and (-5, -9) is (1.5, -6).
Examples
The midpoint formula is useful in various real-world scenarios. For example, if you and a friend are planning to meet at a location that is equidistant from both your homes, you can use the midpoint formula to find that meeting point on a map, given the coordinates of your homes. This ensures a fair and convenient meeting spot for both of you. Another example is in computer graphics, where the midpoint is used to draw lines and curves efficiently.
The midpoint of the line segment with endpoints (8, -3) and (-5, -9) is (1.5, -6). Therefore, the correct answer is option B. (1.5, -6).
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