Find the value of x for which the points (5, -1), (2, 1) and (x, y) are collinear.
Understand the Problem
The question appears to be from a mathematics exercise involving geometry and coordinate systems. It requests the user to find specific values, angles, coordinates, and relationships between points in a two-dimensional plane.
Answer
The midpoint is \( M(7, 2) \).
Answer for screen readers
The midpoint ( M ) is ( (7, 2) ).
Steps to Solve
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Identify the key points We have the points ( A(5, -2) ) and ( B(9, 6) ), which will help us find the midpoint of the line segment joining these points.
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Formula for the midpoint The formula for finding the midpoint ( M ) of two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is given by: $$ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$
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Substituting the points into the formula Using the points ( A(5, -2) ) and ( B(9, 6) ): $$ M = \left( \frac{5 + 9}{2}, \frac{-2 + 6}{2} \right) $$
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Calculating the coordinates Now calculate the x-coordinate and the y-coordinate:
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( x )-coordinate: $$ \frac{5 + 9}{2} = \frac{14}{2} = 7 $$
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( y )-coordinate: $$ \frac{-2 + 6}{2} = \frac{4}{2} = 2 $$
- Final midpoint Therefore, the midpoint ( M ) of the line segment joining the points ( A(5, -2) ) and ( B(9, 6) ) is ( M(7, 2) ).
The midpoint ( M ) is ( (7, 2) ).
More Information
The midpoint of a line segment is a point that is equidistant from both endpoints. Finding midpoints is often used in geometry to simplify problems or to find center points.
Tips
- Miscalculating the average: Make sure to add the coordinates correctly before dividing by 2.
- Forgetting to divide by 2: Always remember that the formula includes division by 2 to obtain the midpoint.
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