The line PQ with equation x - y = 2 intersect | vedclass

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(C) The line $PQ$ has the equation $x - y = 2$,which can be written as $y = x - 2$. The slope $m_1$ of this line is $1$,so the angle of inclination $\

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$x = 2$

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(C) The line $PQ$ has the equation $x - y = 2$,which can be written as $y = x - 2$. The slope $m_1$ of this line is $1$,so the angle of inclination $	heta_1 = 45^{\circ}$.Point $P$ is the intersection with the $x$-axis,found by setting $y = 0$,which gives $x = 2$. Thus,$P = (2, 0)$.The line is rotated by $45^{\circ}$ counter-clockwise about $P$. The new angle of inclination $	heta_2 = 	heta_1 + 45^{\circ} = 45^{\circ} + 45^{\circ} = 90^{\circ}$.$A$ line with an angle of inclination of $90^{\circ}$ is a vertical line. Since it passes through $P(2, 0)$,its equation is $x = 2$.

The line $PQ$ with equation $x - y = 2$ intersects the $x$-axis at $P$. Given $Q$ is $(4, 2)$. Find the equation of the line $PQ$ after it is rotated by $45^{\circ}$ in the counter-clockwise direction about point $P$.

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