Question

What are the possible values of m if the Point p(m, 4) is 5√5 units away from Q (-3,-1).​

Answer 1

To find the possible values of m, we can use the distance formula in a coordinate plane. The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

`\displaystyle\sf d = \sqrt{(x_(2)-x_(1))^2 + (y_(2)-y_(1))^2}`

In this case, we have the point P(m, 4) and the point Q(-3, -1), and the distance between them is 5√5. Plugging the values into the formula, we get:

`\displaystyle\sf 5√(5) = √((-3-m)^2 + (-1-4)^2)`

Simplifying the equation, we have:

`\displaystyle\sf 5√(5) = √((-3-m)^2 + (-5)^2)`

`\displaystyle\sf (5√(5))^2 = (-3-m)^2 + (-5)^2`

`\displaystyle\sf 125 = (-3-m)^2 + 25`

`\displaystyle\sf 125 - 25 = (-3-m)^2`

`\displaystyle\sf 100 = (-3-m)^2`

Taking the square root of both sides, we get:

`\displaystyle\sf √(100) = -3 - m` or
`\displaystyle\sf √(100) = -3 + m`

Simplifying further, we have two possibilities:

`\displaystyle\sf 10 = -3 - m` or
`\displaystyle\sf 10 = -3 + m`

For the first equation, solving for m, we have:

`\displaystyle\sf m = -3 - 10`

`\displaystyle\sf m = -13`

For the second equation, solving for m, we have:

`\displaystyle\sf m = 10 - (-3)`

`\displaystyle\sf m = 13`

Therefore, the possible values of m are
`\displaystyle\sf -13` and
`\displaystyle\sf 13`.

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