Finding Coordinates of Point B Using Midpoint Formula
The problem requires finding the coordinates of point B given the coordinates of point A and the midpoint D of the line segment AB.
Midpoint Formula Explanation
Let the coordinates of A be \((x_1, y_1)\) and the coordinates of B be \((x_2, y_2)\). If D \((x_m, y_m)\) is the midpoint of the line segment AB, the midpoint formula states:
\(x_m = \frac{x_1 + x_2}{2}\) \(y_m = \frac{y_1 + y_2}{2}\)Applying the Formula
Given:
- Coordinates of A: \((x_1, y_1) = (2, 4)\)
- Coordinates of D (midpoint): \((x_m, y_m) = (-1, 3)\)
- Coordinates of B: \((x_2, y_2)\) (to be found)
Calculating the x-coordinate of B:
Substitute the known values into the x-midpoint formula:
\(-1 = \frac{2 + x_2}{2}\)Multiply both sides by 2:
\(-1 \times 2 = 2 + x_2\) \(-2 = 2 + x_2\)Solve for \(x_2\):
\(x_2 = -2 - 2\) \(x_2 = -4\)Calculating the y-coordinate of B:
Substitute the known values into the y-midpoint formula:
\(3 = \frac{4 + y_2}{2}\)Multiply both sides by 2:
\(3 \times 2 = 4 + y_2\) \(6 = 4 + y_2\)Solve for \(y_2\):
\(y_2 = 6 - 4\) \(y_2 = 2\)Result
The coordinates of point B are \((-4, 2)\). This corresponds to Option 3.
Similar Questions
- In which quadrant do the point (-16, 9) lies
- D is the midpoint of line segment AB. The co-ordinates of A and D are (2, 4) and (-1, 3), respectively. The co-ordinates of B are:
Important Questions from Co-ordinate Geometry
The graphs of the linear equations 4x - 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
