Multiple choice

If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length

  1. 3

  2. 4

  3. 6

  4. 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate squared distances between points: A(1,1), B(2,3), C(5,-1). AB^2 = (2-1)^2 + (3-1)^2 = 1+4=5. BC^2 = (5-2)^2 + (-1-3)^2 = 9+16=25. AC^2 = (5-1)^2 + (-1-1)^2 = 16+4=20. Since AB^2 + AC^2 = 5 + 20 = 25 = BC^2, BC is the hypotenuse. Length = sqrt(25) = 5.

AI explanation

Find the lengths of the sides of the triangle using the distance formula. The distance between (1, 1) and (2, 3) is the square root of 5, between (2, 3) and (5, -1) is 5, and between (1, 1) and (5, -1) is the square root of 20. Since (5 squared) plus ((square root of 5) squared) equals (square root of 20 squared), the triangle is right-angled with the side connecting (2, 3) and (5, -1) as the hypotenuse. Therefore, the hypotenuse is 5.

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