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:
The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
What is the area (in unit squares) of the triangle enclosed by the graphs of 2x + 5y = 12, x + y = 3 and the x-axis?
The graphs of the equations 3x - 20y - 2 = 0 and 11x - 5y + 61 = 0 intersect at P(a, b). What is the value of (a 2+ b 2- ab)/(a 2- b 2+ ab)?
The graphs of the linear equations 3x - 2y = 8 and 4x + 3y = 5 intersect at the point P(α, β). What is the value of (2 α - β)?
