Question

find the midpoint of points a(3,6) and b(7, -4) graphically.
plot the line segment ab by clicking twice on the graph.
start over

Explanation:

Step1: Recall midpoint formula

The midpoint \( M(x_m, y_m) \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( x_m=\frac{x_1 + x_2}{2} \), \( y_m=\frac{y_1 + y_2}{2} \).

Step2: Identify coordinates

For \( A(3,6) \), \( x_1 = 3 \), \( y_1 = 6 \); for \( B(7,-4) \), \( x_2 = 7 \), \( y_2=-4 \).

Step3: Calculate x - coordinate of midpoint

\( x_m=\frac{3 + 7}{2}=\frac{10}{2}=5 \).

Step4: Calculate y - coordinate of midpoint

\( y_m=\frac{6+(-4)}{2}=\frac{2}{2}=1 \).

Answer:

The midpoint of \( A(3,6) \) and \( B(7,-4) \) is \( (5,1) \). To plot graphically, plot \( A(3,6) \) and \( B(7,-4) \), then find the point halfway between them, which is \( (5,1) \).