The points (1, 3) and (5, 1) are the opposite | vedclass

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(B) Let $ABCD$ be a rectangle with opposite vertices $A(1, 3)$ and $C(5, 1)$.Since the diagonals of a rectangle bisect each other,the intersection poi

Vedclass · Accepted Answer

$-4$

Vedclass · Answer

(B) Let $ABCD$ be a rectangle with opposite vertices $A(1, 3)$ and $C(5, 1)$.Since the diagonals of a rectangle bisect each other,the intersection point of the diagonals is the midpoint of $AC$.Midpoint of $AC = \left(\frac{1+5}{2}, \frac{3+1}{2}\right) = (3, 2)$.The other two vertices $B$ and $D$ lie on the line $y = 2x + c$. Since the diagonal $BD$ passes through the intersection point of the diagonals,the point $(3, 2)$ must lie on the line $y = 2x + c$.Substituting $x = 3$ and $y = 2$ into the equation:$2 = 2(3) + c$$2 = 6 + c$$c = 2 - 6 = -4$.Thus,the value of $c$ is $-4$.

The points $(1, 3)$ and $(5, 1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$. Then the value of $c$ is:

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