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The coordinates of square ABCD are A(0, 0) , B(a, 0) , C(blank, a), and D(0,blank ).

The slope of AC, when simplified, is equal to blank .

The slope of BD, when simplified, is equal to −1 .

The product of the slopes is equal to blank .

Therefore, AC is perpendicular to BD.

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The coordinates of square ABCD are A0 0 Ba 0 Cblank a and D0blank The slope of AC when simplified is equal to blank The slope of BD when simplified is equal to class=

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choixongdong
The coordinates of square ABCD are A(0, 0) , B(a, 0) , C(blank, a), and D(0,blank ).

square, all sides are equal so side = a
A(0, 0) , B(a, 0) , C(a, a), and D(0,a).

The slope of AC = (a-0)/(a-0) = a/a = 1
The slope of BD, when simplified, is equal to −1

The product of the slopes = 1(-1) = -1

Therefore, AC is perpendicular to BD.

This is about finding slopes of lines.

The slope of AC, when simplified = 1

The product of the slopes = -1

  • ABCD is a square.

All sides of a square are equal.

This means that;

If AB = a, then it means;

AB = BC = CD = AD = a

  • Point D is on the y-axis and so coordinate of D is; (0, a)

While coordinate of C is; (a, a)

Thus coordinates of each point of the square are;

A(0, 0) , B(a, 0) , C(a, a) and D(0, a)

  • Formula for slope between two coordinates is; m = (y2 - y1)/(x2 - x1)

Thus;

  • The slope of AC = (a - 0)/(a - 0) = a/a = 1

  • The slope of BD, when simplified, is equal to −1

  • The product of the slopes of AC and BD = 1 × (-1) = -1

  • Therefore, AC is perpendicular to BD.:

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