Question

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

(-3,6), (1,-4)

Answer 1

The distance between the points (-3,6) and (1,-4) is approximately 11.7 units.

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula, which is given by:

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

In this formula,
`\((x_1, y_1)\) and \((x_2, y_2)\)` are the coordinates of the two points. For the given points (-3,6) and (1,-4), we can substitute these values into the formula:

`\[ d = \sqrt{{(1 - (-3))^2 + ((-4) - 6)^2}} \]`

Simplifying this expression:

`\[ d = \sqrt{{4^2 + (-10)^2}} \]`

`\[ d = \sqrt{{16 + 100}} \]`

`\[ d = \sqrt{{116}} \]`

Now, to find the decimal approximation, we take the square root of 116:

`\[ d ≈ 10.7703 \]`

Rounding to the nearest tenth, the distance is approximately 11.7 units.

In conclusion, the distance between the points (-3,6) and (1,-4) is approximately 11.7 units. This result is obtained using the distance formula, which calculates the straight-line distance between two points in a coordinate plane.