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The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD. Equation of a Line, Concise Mathematics Solutions ICSE Class 10.

Straight Line Eq

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Answer

From figure,

Slope of AB = tan 45° = 1.

Slope of CD = tan 60° = 3\sqrt{3}.

By point-slope form,

yy1=m(xx1)y - y1 = m(x - x1)

Since, line AB passes through point P(3, 4) and slope = 1. Substituting values in point-slope form,

⇒ y - 4 = 1(x - 3)

⇒ y - 4 = x - 3

⇒ y - x = -3 + 4

⇒ y - x = 1

⇒ y = x + 1.

Since, line CD passes through point P(3, 4) and slope = 3\sqrt{3}. Substituting values in point-slope form,

⇒ y - 4 = 3\sqrt{3}(x - 3)

⇒ y - 4 = 3x33\sqrt{3}x - 3\sqrt{3}

⇒ y = 3x33+4\sqrt{3}x - 3\sqrt{3} + 4.

Hence, equation of AB is y = x + 1 and equation of CD is y = 3x33+4\sqrt{3}x - 3\sqrt{3} + 4.

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