Question

What is the distance between (3,10) and (3,−8) on a coordinate grid?

Answer 1

To find the distance between the points (3,10) and (3,−8) which have the same x-coordinate, simply subtract the y-coordinates and take the absolute value. The distance is 18 units since they are aligned vertically.

Step-by-step explanation:

The distance between two points on a coordinate grid is calculated using the distance formula, which is derived from the Pythagorean theorem. However, if both points have the same x-coordinate or the same y-coordinate, the calculation becomes simpler since we are dealing with a straight line either horizontally or vertically. In this case, the points (3,10) and (3,−8) have the same x-coordinate, which means they are vertical from each other on the grid.

To find the distance between these two points, we need to calculate the absolute difference between their y-coordinates. The distance can be found using the following steps:

1. Identify the y-coordinates of the two points: y1 = 10 and y2 = −8.
2. Subtract the smaller y-coordinate from the larger y-coordinate: 10 - (−8) = 10 + 8.
3. Calculate the absolute value: |10 + 8| = |18|.
4. The distance is therefore 18 units on the coordinate grid.

This means that the points are 18 units apart vertically. Remember, the negative sign in the y-coordinate indicates a position below the x-axis, while a positive y-coordinate indicates a position above the x-axis on a standard Cartesian plane.