Question

Find the exact distance between the points. (−4,4) and (−9,−1) a)178 b)50 c)√178 ​d)5√2

Answer 1

The exact distance between the points (-4, 4) and (-9, -1) is 5√2,So, the correct option is d.

Step-by-step explanation:

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

`\[d = √((x_2 - x_1)^2 + (y_2 - y_1)^2).\]`

In this case, let
`\((x_1, y_1) = (-4, 4)\)`and
`\((x_2, y_2) = (-9, -1)\).` Substituting these values into the formula:

`\[d = √((-9 - (-4))^2 + ((-1) - 4)^2).\]`

Simplifying further:

`\[d = √((-5)^2 + (-5)^2) = √(25 + 25) = √(50).\]`

To express the answer in the required format, we can simplify
`\(√(50)\)` as
`(5√(2)\)` since
`\(√(50) = √(25 * 2) = 5√(2)\).` Therefore, the final answer is
`(5√(2)\).`

In summary, the distance between the points (-4, 4) and (-9, -1) is
`(5√(2)\)`.obtained by applying the distance formula and simplifying the square root expression. This result indicates the length of the straight line segment connecting the two points in the Cartesian plane,Thus, the correct option is d.