The vertices of a square ABCD are given as A (x $_{1}$ , y $_{1}$ ), B (x $_{2}$ , y $_{2}$ ), C (x $_{3}$ , y $_{3}$ ) and D (x $_{4}$ , y $_{4}$ ).
Which of the following will always hold true?

x₁ + y₁ = x₂+y₂

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x₁ +x₂ =y₁ + y₂

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x₁ +x₃ = x₂ +x₄

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x₁ + y₂ = x₂+y₁

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x₁ + x₄ = y₁+y₄

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Solution

The correct option is C
x₁ +x₃ = x₂ +x₄

In a square the midpoints of the diagonals is the same.
If A (x $_{1}$ , y $_{1}$ ), B (x $_{2}$ , y $_{2}$ ), C (x $_{3}$ , y $_{3}$ ) and D (x $_{4}$ , y $_{4}$ ) are the vertices of a square ABCD, then the midpoints of AC and BD is the same.
$∴$ x $_{1}$ + x $_{3}$ = x $_{2}$ + x $_{4}$

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The vertices of a square ABCD are given as A (x1, y1), B (x2, y2), C (x3, y3) and D (x4, y4). Which of the following will always hold true?

The correct option is C x1 +x3 = x2 +x4 In a square the midpoints of the diagonals is the same. If A (x1, y1), B (x2, y2), C (x3, y3) and D (x4, y4) are the vertices of a square ABCD, then the midpoints of AC and BD is the same. ∴ x1 + x3 = x2 + x4

The vertices of a square ABCD are given as A (x $_{1}$ , y $_{1}$ ), B (x $_{2}$ , y $_{2}$ ), C (x $_{3}$ , y $_{3}$ ) and D (x $_{4}$ , y $_{4}$ ).
Which of the following will always hold true?