The line 2x + y = 4 intersects the X and Y ax | vedclass

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(B) Step $1$: Find the coordinates of $A$ and $B$. For $X$-axis, set $y=0$: $2x = 4 \implies x=2$. So $A = (2, 0)$. For $Y$-axis, set $x=0$: $y=4$. So

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$\sqrt{5}$

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(B) Step $1$: Find the coordinates of $A$ and $B$. For $X$-axis, set $y=0$: $2x = 4 \implies x=2$. So $A = (2, 0)$. For $Y$-axis, set $x=0$: $y=4$. So $B = (0, 4)$.Step $2$: Find the midpoint $M$ of $AB$. $M = (\frac{2+0}{2}, \frac{0+4}{2}) = (1, 2)$.Step $3$: Since $AC \perp BC$, point $C$ lies on a circle with diameter $AB$. The center of this circle is the midpoint $M(1, 2)$.Step $4$: The radius $r$ of this circle is the distance $MA = \sqrt{(2-1)^2 + (0-2)^2} = \sqrt{1^2 + (-2)^2} = \sqrt{1+4} = \sqrt{5}$.Step $5$: Since $C$ lies on the circle, the distance from $C$ to the center $M$ is equal to the radius $r = \sqrt{5}$.

The line $2x + y = 4$ intersects the $X$ and $Y$ axes at points $A$ and $B$ respectively. Let $C(p, q)$ be a point such that the lines $AC$ and $BC$ are perpendicular. Find the distance of point $C$ from the midpoint of segment $AB$.

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