If the midpoints of the sides BC, CA and AB o | vedclass

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(B) Let the midpoints be $E(1, 3)$ on $BC$,$D(5, 7)$ on $CA$,and $F(-5, 7)$ on $AB$.By the midpoint theorem,the line segment joining the midpoints of

Vedclass · Accepted Answer

$x - y + 12 = 0$

Vedclass · Answer

(B) Let the midpoints be $E(1, 3)$ on $BC$,$D(5, 7)$ on $CA$,and $F(-5, 7)$ on $AB$.By the midpoint theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side.Therefore,the side $AB$ is parallel to the line segment $ED$.The slope of $ED = \frac{7 - 3}{5 - 1} = \frac{4}{4} = 1$.Since $AB$ is parallel to $ED$,the slope of $AB$ is also $1$.The side $AB$ passes through the midpoint $F(-5, 7)$.The equation of line $AB$ is given by $y - y_1 = m(x - x_1)$.Substituting the values,$y - 7 = 1(x - (-5))$.$y - 7 = x + 5$.$x - y + 12 = 0$.

If the midpoints of the sides $BC, CA$ and $AB$ of the triangle $ABC$ are $(1, 3), (5, 7)$ and $(-5, 7)$ respectively,then the equation of the side $AB$ is

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