The points A (1, 3) and C (5, 1) are the oppo | vedclass

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(B) Let the rectangle be $ABCD$. The points $A (1, 3)$ and $C (5, 1)$ are opposite vertices.The midpoint of the diagonal $AC$ is $M = (\frac{1+5}{2},

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$2x - y - 4 = 0$

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(B) Let the rectangle be $ABCD$. The points $A (1, 3)$ and $C (5, 1)$ are opposite vertices.The midpoint of the diagonal $AC$ is $M = (\frac{1+5}{2}, \frac{3+1}{2}) = (3, 2)$.Since $M$ is the center of the rectangle,it must also lie on the diagonal $BD$ connecting the other two vertices.The line passing through the other two vertices ($B$ and $D$) has a gradient $m = 2$.Using the point-slope form $y - y_1 = m(x - x_1)$ for the line passing through $M (3, 2)$ with slope $m = 2$:$y - 2 = 2(x - 3)$$y - 2 = 2x - 6$$2x - y - 4 = 0$.

The points $A (1, 3)$ and $C (5, 1)$ are the opposite vertices of a rectangle. The equation of the line passing through the other two vertices and having a gradient of $2$ is:

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