Question

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. \((1,12),(6,0)\)

Short answer

The plotted points are (1,12) and (6,0). The distance between the points is 13 units. The midpoint of the line segment joining the points is (3.5, 6).

Step-by-step solution

Plotting the Points

Plot the points (1,12) and (6,0) on a 2D coordinate grid.

Compute the Distance

Use the distance formula d = \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Substituting the given points into this formula we get d = \( \sqrt{(6 - 1)^2 + (0 - 12)^2} \) = \( \sqrt{25 + 144} \) = \( \sqrt{169} \) = 13.

Compute the Midpoint

Midpoint is calculated using the formula M = \(\left(\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}\right)\). Substituting the values of the given points, we get M = \(\left(\frac{(1 + 6)}{2}, \frac{(12 + 0)}{2}\right)\) = (3.5, 6).