Question

The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. P (n, 3). Point Q is graphed at (n, 2). The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.

Answer 1

The distance from point P to point Q is sqrt(2) units. The value of n is -3.

Step-by-step explanation:

From the graph, we can see that point P is located at (n, 3) and point R is on the y-axis with the same y-coordinate as point P. Point Q is graphed at (n, 2).

To determine the distance from point P to point Q, we can use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the coordinates, we have d = sqrt((n - n)^2 + (2 - 3)^2) = sqrt((-1)^2 + (-1)^2) = sqrt(2).

Since the distance from point P to point Q is equal to the distance from point P to point R, we can set up the equation sqrt((n - n)^2 + (2 - 3)^2) = sqrt(n^2 + 3^2). After simplifying, we get sqrt((-1)^2 + (-1)^2) = sqrt(n^2 + 9). Squaring both sides, we have (-1)^2 + (-1)^2 = n^2 + 9. This simplifies to 2 = n^2 + 9. Solving for n, we get n = -3.