A(5,2), B(3,4) and C(x, y) are collinear and | vedclass

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(B) Given that points $A, B$ and $C$ are collinear and $AB = BC$.This implies that point $B$ is the midpoint of the line segment $\overline{AC}$.Using

Vedclass · Accepted Answer

$(1,6)$

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(B) Given that points $A, B$ and $C$ are collinear and $AB = BC$.This implies that point $B$ is the midpoint of the line segment $\overline{AC}$.Using the midpoint formula,the coordinates of $B$ are given by $\left(\frac{x_A + x_C}{2}, \frac{y_A + y_C}{2}\right)$.Substituting the given values: $(3, 4) = \left(\frac{5 + x}{2}, \frac{2 + y}{2}\right)$.Equating the $x$-coordinates: $\frac{5 + x}{2} = 3 \implies 5 + x = 6 \implies x = 1$.Equating the $y$-coordinates: $\frac{2 + y}{2} = 4 \implies 2 + y = 8 \implies y = 6$.Therefore,the coordinates of point $C$ are $(1, 6)$.

$A(5,2), B(3,4)$ and $C(x, y)$ are collinear and $AB = BC$,then the coordinates of $C$ are...............

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