Question

What is the distance between the points ( -4, 6) and (-4, -2)

Answer 1

Find the gradient then choose one of the pairs of the points then substitute y to find x

Answer 2

8

Explanation:

The distance between two points
`\((x_1, y_1)\)` and
`\((x_2, y_2)\)` in a coordinate system can be found using the distance formula:

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

In this case, the points are
`\((-4, 6)\)` and
`\((-4, -2)\)`. Let's plug these values into the formula:

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

Simplifying:

`\[ d = \sqrt{{0^2 + (-8)^2}} \]`

`\[ d = \sqrt{{64}} \]`

`\[ d = 8 \]`

So, indeed, the distance between the points
`\((-4, 6)\)` and
`\((-4, -2)\)` is 8.