The midpoint of the line segment joining A(2, 4) and B(x, 10) is (6, 7). Find the value of x.
10
The midpoint formula for points \(A(x_1, y_1)\) and \(B(x_2, y_2)\) is \(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\).
For \(A(2,4)\) and \(B(x,10)\), the midpoint is \((6,7)\).
Using the x-coordinate: \(\frac{2+x}{2} = 6 \Rightarrow 2+x = 12 \Rightarrow x = 10\).
Checking with the y-coordinate: \(\frac{4+10}{2} = 7\), which matches.
Hence, \(x = 10\).
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).
