Question

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. \((2,10),(10,2)\)

Short answer

The distance between points \((2,10)\) and \((10,2)\) is \(\sqrt{64}\) or 8 units. The midpoint of the line segment joining these points is \( (6,6) \).

Step-by-step solution

Plotting Points

One needs to plot the points \((2,10)\) and \((10,2)\) on a coordinate plane. The first coordinate represents the x-value and the second coordinate refers to the y-value.

Calculating Distance

Apply the distance formula derived from the Pythagorean theorem, which is \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\). Here, \(x_1 = 2, y_1 = 10, x_2 = 10\), and \(y_2 = 2\). Substitute these values into the formula and simplify to find the distance.

Calculating Midpoint

The midpoint formula is \((\frac{x1+x2}{2}, \frac{y1+y2}{2})\). Substitute \(x_1 = 2, y_1 = 10, x_2 = 10\), and \(y_2 = 2\) into the formula and simplify to find the midpoint.