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

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

Graphically, we can plot points \( A(3,6) \) and \( B(7,-4) \), then draw the line segment \( AB \). The midpoint will be the point on \( AB \) that is equidistant from \( A \) and \( B \), which we found to be \( (5,1) \) using the formula, and this can be verified by measuring the distances or by the midpoint's position on the graph.

Answer:

The midpoint of points \( A(3,6) \) and \( B(7,-4) \) is \( (5,1) \).