Question

whats midpoint of points A, left parenthesis, 2, comma, 6, right parenthesisA(2,6) and B, left parenthesis, 9, comma, 0, right parenthesisB(9,0) graphically.

Answer 1

To find the midpoint of the points A(2, 6) and B(9, 0) graphically, you can follow these steps:

1. **Plot the Points**: Start by plotting the points A(2, 6) and B(9, 0) on a Cartesian coordinate system.

2. **Draw a Line Segment**: Draw a straight line connecting points A and B.

3. **Find the Midpoint**: The midpoint M of a line segment that connects two points \(A(x_1, y_1)\) and \(B(x_2, y_2)\) is given by the formula:
\[
M\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Applying this formula:
- Coordinates of A are \(x_1 = 2\), \(y_1 = 6\)
- Coordinates of B are \(x_2 = 9\), \(y_2 = 0\)

Substitute these values into the midpoint formula:
\[
M\left( \frac{2 + 9}{2}, \frac{6 + 0}{2} \right) = M\left( \frac{11}{2}, \frac{6}{2} \right) = M\left( 5.5, 3 \right)
\]

4. **Mark the Midpoint**: On your graph, plot the point \(M(5.5, 3)\). This point represents the midpoint of segment AB.

Thus, graphically, the midpoint M between points A(2, 6) and B(9, 0) is located at \(M(5.5, 3)\).