If A(2, -3) and C(-6, 7) are opposite vertice | vedclass

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(C) Step $1$: The diagonals of a rhombus are perpendicular bisectors of each other.Step $2$: Find the midpoint $M$ of diagonal $AC$: $M = (\frac{2 - 6

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$4x - 5y + 18 = 0$

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(C) Step $1$: The diagonals of a rhombus are perpendicular bisectors of each other.Step $2$: Find the midpoint $M$ of diagonal $AC$: $M = (\frac{2 - 6}{2}, \frac{-3 + 7}{2}) = (-2, 2)$.Step $3$: Find the slope of diagonal $AC$: $m_{AC} = \frac{7 - (-3)}{-6 - 2} = \frac{10}{-8} = -\frac{5}{4}$.Step $4$: The slope of diagonal $BD$ is the negative reciprocal of $m_{AC}$: $m_{BD} = -\frac{1}{m_{AC}} = \frac{4}{5}$.Step $5$: The equation of line $BD$ passing through $M(-2, 2)$ with slope $m = \frac{4}{5}$ is $y - 2 = \frac{4}{5}(x + 2)$.Step $6$: Simplify the equation: $5(y - 2) = 4(x + 2) \implies 5y - 10 = 4x + 8 \implies 4x - 5y + 18 = 0$.

If $A(2, -3)$ and $C(-6, 7)$ are opposite vertices of a rhombus $ABCD$, then the equation of diagonal $BD$ is

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