College Algebra Final Exam Review – Step-by-Step Guidance

Q19. Find the distance $d(P_1, P_2)$ between the points $P_1$ and $P_2$.

Background

Topic: Distance Formula in Coordinate Geometry

This question tests your ability to use the distance formula to find the length between two points in the Cartesian plane.

Key formula:

The distance between two points $P_1 = (x_1, y_1)$ and $P_2 = (x_2, y_2)$ is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• $x_1, y_1$ = coordinates of the first point

• $x_2, y_2$ = coordinates of the second point

Step-by-Step Guidance

1. Identify the coordinates of $P_1$ and $P_2$ from the graph. Carefully read the values for $x$ and $y$ for each point.

2. Write down the coordinates as $P_1 = (x_1, y_1)$ and $P_2 = (x_2, y_2)$.

3. Substitute these values into the distance formula:

   $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

4. Calculate $(x_2 - x_1)$ and $(y_2 - y_1)$, then square each result.

Try solving on your own before revealing the answer!

Final Answer: $d(P_1, P_2) = 10.6$

Using the coordinates from the graph and the distance formula, the distance between the points is approximately 10.6 units.