Question

Distance between points (1,2) and (4,6) is:

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

This formula is just the Pythagorean theorem in disguise. The distance is the hypotenuse of a right-angled triangle with base 3 and height 4. (3-4-5 is a famous Pythagorean triple).

Answer 1

The Correct Option is C

To find the distance between two points, we use the distance formula. The distance between points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Given points are \((1, 2)\) and \((4, 6)\).

1. Identify the coordinates: \((x_1, y_1) = (1, 2)\) and \((x_2, y_2) = (4, 6)\).
2. Substitute these coordinates into the formula:

\(d = \sqrt{{(4 - 1)^2 + (6 - 2)^2}}\)

1. Simplify the equation:

\(d = \sqrt{{3^2 + 4^2}}\)

1. Calculate the squares:

\(d = \sqrt{{9 + 16}}\)

1. Add the results:

\(d = \sqrt{25} = 5\)

Thus, the distance between the points \((1, 2)\) and \((4, 6)\) is 5. Therefore, the correct answer is 5.