If Point A Is (4, –1) And Point B Is (3, 5), What Is The Square Of The Distance AB² Between Them?

If point A is (4, –1) and point B is (3, 5), what is the square of the distance AB² between them?

Explanation

To find the square of the distance between two points $A(x_1, y_1)$ and $B (x_{2}, y_{2})$ :

$A B^^{2} = (x_{2} - x_{1})^^{2} + (y_{2} - y_{1})^^{2}$ $= (3 - 4)^2 + (5 - (-1))^2 = (-1)^2 + (6)^2 = 1 + 36 = 37$

$= (- 1)^^{2} + (6)^^{2}$

$= 1 + 36$

$= 37$

Related MCQs

If the point is (a,−a), then it lies on which line?

y=x
y=−x
y=a
x=a

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Find the sum: 2×1^2 +4×2^2 +6×3^ +⋯+20×10^2

76,440
77,000
77,440
6050

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Explanation

Given:

2 \times 1^^{2} + 4 \times 2^^{2} + 6 \times 3^^{2} + \dots + 20 \times 1 0^2

Write the terms as:

2 (1^^{3}) + 2 (2^^{3}) + 2 (3^^{3}) + \dots + 2 (1 0^^{3})

= 2 (1^^{3} + 2^^{3} + 3^^{3} + \dots + 1 0^^{3})

Using the formula:

1^3+2^3+cdots+n^3=left[frac{n(n+1)}{2}right]^2

For $n = 10$ :

= 2 [10 ( 11 )/2]^^{2}

= 2 (55)^^{2}

= 2 \times 3025

6050

$Last updated 27-07-2026 by NA$

If x+y=16 and x−y=3, then x^2 −^ 2 =?

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Explanation

Given:

$x + y = 16$
$x-y=3$

Using the identity:

$x^{2} - y^{2} = (x + y) (x - y)$ $= 16 \times 3$

$= 48$

$Last updated 27-07-2026 by NA$

If y is directly proportional to x and x = 2, y = 5, then find y when x = 7?

15
35/2
25/2
None of these

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The volume of a cube is 275. The length of one side of the cube is?

∛275
275²
275 ÷ 3
None of these

If point A is (4, –1) and point B is (3, 5), what is the square of the distance AB² between them?

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If point A is (4, –1) and point B is (3, 5), what is the square of the distance AB² between them?

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