Question
Download Solution PDFIf the distance between the points (x, -1) and (3, 2) is 5 units, then what will be the value of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept -
The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane is given by the distance formula:
\( \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Explanation -
Here, the points are (x, -1) and (3, 2), and the distance is given as 5 units. Using the distance formula:
\(5 = \sqrt{(3 - x)^2 + (2 - (-1))^2} \\ 5 = \sqrt{(3 - x)^2 + 3^2} \\ 5 = \sqrt{(3 - x)^2 + 9} \)
let's square both sides to eliminate the square root:
\( 5^2 = (3 - x)^2 + 9 \\ 25 = (3 - x)^2 + 9 \\ (3 - x)^2 = 25 - 9 \\ (3 - x)^2 = 16 \)
Now, take the square root of both sides:
\( 3 - x = \pm \sqrt{16} \\ 3 - x = \pm 4 \)
Solve for x in both cases:
When 3 - x = 4:
x = 3 - 4
x = -1
When 3 - x = -4:
x = 3 + 4
x = 7
So, the values for x are x = -1 or x = 7.
Last updated on Jan 29, 2025
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