Question

If (2,1), (-1, -2), (3,3) are mid points of sides BD, DA, AB of ΔABD then equation of side BD is

A)
5x + 4y - 14 = 0

B)
2x + y - 5 = 0

C)
x - 2y = 0

D)
5x - 4y - 6 = 0​

Answer 1

Answer:

OPTION D) 5x - 4y - 6 = 0

Step-by-step explanation:

E( 2 , 1 ) , F( - 1 , - 2 ) and G( 3 , 3 ) are the midpoints of the sides BD , DA and AB of the ∆ABD .

$\sf </p><p>\: We \: know\: that </p><p>\\ \\ \sf By \: midpoint\: theorem </p><p></p><p></p><p>\\ \\ \sf GF || BD </p><p></p><p>\\ \\ \sf </p><p>Hence </p><p></p><p>\\ \\ </p><p>\sf slope \: of \: GF = slope \: of \: BD </p><p></p><p>\\ \\ </p><p>\sf Slope\: of \: GF = \frac { {y}_{2} - {y}_{1}}{{x}_{2} -{x}_{1}} \\ \\ \sf = \frac {3 - ( - 2) }{ 3 - (-1)} \\ \\ \sf = \frac{5}{4} \\ \\ \sf Hence \: slope \:of \: BD = \frac{5}{4} \\ \\ \sf We\:have\:point\:E \: on \: the \: side BD \\ \\ \sf so \: by \: point \: slope \: form \\ \\ \sf Equation \: of \: BD \\ \\ \sf y - {y}_{1} = m( x - {x}_{1}) \\ \\ \sf y - 1 = \frac {5}{4} ( x - 2 ) \\ \\ \sf 4y - 4 = 5x - 10 \\ \\ \sf 5x - 4y - 6 = 0$