The coordinates of AB are A(-2,5) and B(4,-8). If point C is 1/3 the length of directed segment AB, what are the coordinates of point C?
Answer (2)
Find the midpoint C of the line segment A B .
Use the midpoint formula: x C = 2 x A + x B and y C = 2 y A + y B .
Substitute the coordinates of A ( − 2 , 5 ) and B ( 4 , − 8 ) into the midpoint formula.
Calculate the coordinates of point C : ( 1 , − 1.5 ) .
Explanation
Analyze the problem and data The problem states that the coordinates of point A are (-2, 5) and the coordinates of point B are (4, -8). We are asked to find the coordinates of point C, given that C is the length of the directed segment AB. This statement is ambiguous. Let's assume that C is the midpoint of the segment AB.
Apply the midpoint formula To find the midpoint C of the segment AB, we use the midpoint formula:
x C = 2 x A + x B and y C = 2 y A + y B
Substituting the given coordinates:
x C = 2 − 2 + 4 = 2 2 = 1
y C = 2 5 + ( − 8 ) = 2 − 3 = − 1.5
State the coordinates of point C Therefore, the coordinates of point C, the midpoint of segment AB, are (1, -1.5).
Examples
In computer graphics, finding the midpoint between two points is essential for drawing lines and curves. For instance, if you want to draw a line between two points A and B on a screen, the midpoint can be used to divide the line into smaller segments for rendering or animation purposes. This ensures smooth transitions and accurate representations of shapes and objects in graphical applications.
Point C, located 1/3 of the distance along the directed segment AB from A(-2, 5) to B(4, -8), has coordinates (0, 0.67). This was calculated by determining the changes in the coordinates from A to B and applying those changes accordingly. In summary, point C is approximately at (0, 0.67).
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