Question

find the midpoint of points a(1,10) and b(7,3) graphically. you may press submit or click the graph again to replot the midpoint.

Explanation:

Step1: Recall midpoint formula

The midpoint \( M(x_m, y_m) \) between 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 \( A(1, 10) \), \( x_1 = 1 \), \( y_1 = 10 \); for \( B(7, 3) \), \( x_2 = 7 \), \( y_2 = 3 \).

Step3: Calculate x - coordinate of midpoint

\( x_m=\frac{1 + 7}{2}=\frac{8}{2}=4 \).

Step4: Calculate y - coordinate of midpoint

\( y_m=\frac{10 + 3}{2}=\frac{13}{2}=6.5 \).

Graphically, we can also visualize the horizontal and vertical distances between the points. The horizontal distance between \( x = 1 \) and \( x = 7 \) is \( 7 - 1=6 \), so half of that is \( 3 \), and \( 1+3 = 4 \) (x - coordinate of midpoint). The vertical distance between \( y = 10 \) and \( y = 3 \) is \( 10 - 3 = 7 \), half of that is \( 3.5 \), and \( 3+3.5 = 6.5 \) (y - coordinate of midpoint).

Answer:

The midpoint of points \( A(1, 10) \) and \( B(7, 3) \) is \( (4, 6.5) \)