Question

(6,1),(8,2) and (9,4) are three vertices of a parallelogram taken in order. find the 4th vertex​

Answer 1

Given :-

• Three vertices of a Parallelogram are (6,1) , (8,2) (9,4)

To find :-

• Other vertex of a parallelogram

Formula to know :-

If ${(x_1,y_1)}$, ${(x_2, y_2)}$, ${(x_3,y_3)}$ are the vertices of a parallelogram then fourth vertex of parallelogram is

Other vertex = ${(x_1 + x_3 - x_2 , y_1 + y_3 - y_2)}$

Solution :-

Just substituting values in formula

${x_1 = 6}$

${x_2 = 8}$

${x_3 = 9}$

${y_1 = 1}$

${y_2 = 2}$

${y_3 = 4}$

Other vertex = ${(x_1 + x_3 - x_2 , y_1 + y_3 - y_2)}$

Fourth vertex = ${(6 + 9 - 8 , 1 + 4 - 2)}$

Fourth vertex = ${(15-8 , 5-2)}$

Fourth vertex = ${(7, 3)}$

So, fourth vertex of a parallelogram is (7,3)

Know more :-

Distance formula:-

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Centroid formula:-

$\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}$

Section formula Internal division:-

$\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}$

Section formula External division :-

$\dfrac{mx_2-nx_1}{m-n}, \dfrac{my_2-ny_1}{m-n}$

Mid point formula :-

$\dfrac{x_1 +x_2 }{2} , \dfrac{y_1 + y_2}{2}$