Question

If the mid point of a line segment joining the points \( (h, 3) \) and \( (6, 5) \) is \( (4, 4) \), then find the value of h.

Hint:

To find the value of an unknown coordinate in a midpoint problem, use the midpoint formula and solve for the missing coordinate.

Answer 1

Step 1: Use the midpoint formula.}
The formula for the midpoint of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Step 2: Substitute the known values.}
Let the points be \( (h, 3) \) and \( (6, 5) \). The midpoint is \( (4, 4) \). For the x-coordinate: \[ \frac{h + 6}{2} = 4 \]
Step 3: Solve for h.}
Multiply both sides by 2: \[ h + 6 = 8 \] Subtract 6 from both sides: \[ h = 8 - 6 = 2 \] % Final Answer Final Answer:
The value of \( h \) is \( 2 \).