The set of all points that forms a triangle o | vedclass

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(B) Let the third vertex be $C(x, y)$. The area of the triangle formed by $A(1, -2)$,$B(-5, 3)$,and $C(x, y)$ is given by:$\Delta = \frac{1}{2} |x_1(y

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$(5x + 6y - 23)(5x + 6y + 37) = 0$

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(B) Let the third vertex be $C(x, y)$. The area of the triangle formed by $A(1, -2)$,$B(-5, 3)$,and $C(x, y)$ is given by:$\Delta = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 15$$\frac{1}{2} |1(3 - y) + (-5)(y - (-2)) + x(-2 - 3)| = 15$$|3 - y - 5y - 10 - 5x| = 30$$|-5x - 6y - 7| = 30$$|5x + 6y + 7| = 30$This implies $5x + 6y + 7 = 30$ or $5x + 6y + 7 = -30$.Thus,$5x + 6y - 23 = 0$ or $5x + 6y + 37 = 0$.The locus of the points is the union of these two lines,which can be written as:$(5x + 6y - 23)(5x + 6y + 37) = 0$.

The set of all points that forms a triangle of area $15$ sq units with the points $(1, -2)$ and $(-5, 3)$ lies on

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