Question

question
find the midpoint of points a(-2,1) and b(4,-3) graphically.
you may press submit or click the graph again to replot the midpoint.

Explanation:

Step1: Recall midpoint formula

The midpoint \( M(x_m, y_m) \) 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 \( A(-2,1) \), \( x_1=-2 \), \( y_1 = 1 \); for \( B(4,-3) \), \( x_2 = 4 \), \( y_2=-3 \).

Step3: Calculate x - coordinate of midpoint

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

Step4: Calculate y - coordinate of midpoint

\( y_m=\frac{1+(-3)}{2}=\frac{-2}{2}=-1 \).
So the midpoint is \( (1, -1) \). To find it graphically, we can also plot the points, draw the line segment between them, and find the point that is halfway in both x - direction (from \( x=-2 \) to \( x = 4 \), the midpoint x is \( \frac{-2 + 4}{2}=1 \)) and y - direction (from \( y = 1 \) to \( y=-3 \), the midpoint y is \( \frac{1+(-3)}{2}=-1 \)).

Answer:

(1, -1)