Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)

Accepted Answer

Identify the coordinates of points P and Q: P has coordinates (-5, -6) and Q has coordinates (7, -1). To find the distance d(P, Q) between points P and Q, use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where $$(x_1$, y_1$)$$ are the coordinates of P and $$(x_2$, y_2$)$$ are the coordinates of Q. Substitute the coordinates into the distance formula: $$d = \sqrt{(7 - (-5))^2 + (-1 - (-6))^2}$$ and simplify inside the parentheses. To find the midpoint M of the line segment PQ, use the midpoint formula: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ where $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$ are the coordinates of P and Q respectively. Substitute the coordinates into the midpoint formula: $$M = \left( \frac{-5 + 7}{2}, \frac{-6 + (-1)}{2} \right)$$ and simplify the expressions inside the parentheses to find the midpoint coordinates.

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)

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Key Concepts

Distance Formula

Midpoint Formula

Coordinate Geometry Basics