Question
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 $CD.$
✓
Answer
Slope of line $AB = \tan 45^\circ = 1$
The line $AB$ passes through $P (3, 4).$ So, the equation of the line $AB$ is given by:
$y − y_1 = m (x − x_1)$
$y − 4 = 1(x − 3)$
$y − 4 = x − 3$
$y = x + 1$
Slope of line $C D=\tan 60^{\circ}=\sqrt{3}$
The line $CD$ passes through $P (3, 4).$
So, the equation of the line $CD$ is given by:
$y − y_1 = m (x − x_1)$
$y-4=\sqrt{3}(x-3)$
$y-4=\sqrt{3} x-3 \sqrt{3}$
$y=\sqrt{3} x+4-3 \sqrt{3}$
The line $AB$ passes through $P (3, 4).$ So, the equation of the line $AB$ is given by:
$y − y_1 = m (x − x_1)$
$y − 4 = 1(x − 3)$
$y − 4 = x − 3$
$y = x + 1$
Slope of line $C D=\tan 60^{\circ}=\sqrt{3}$
The line $CD$ passes through $P (3, 4).$
So, the equation of the line $CD$ is given by:
$y − y_1 = m (x − x_1)$
$y-4=\sqrt{3}(x-3)$
$y-4=\sqrt{3} x-3 \sqrt{3}$
$y=\sqrt{3} x+4-3 \sqrt{3}$
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