you basically find the equation of the line first and eliminate the wrong answers...
Strategy: before u do any of this, label your coordinates as (X1,Y1) and (X2,Y2) and u can choose any of ur points to be as x1 or x2 or y1 or y1... basically, I'll choose (6,7) as (x1,y1) and (2,-1) as (x2,y2). SO,
First you have to find the gradient (m) of the line. you do this by using the formula m = Y2-Y1 / X2-X1 (where '/' is division sign) .... Put the numbers in their respective places and your gradient will be 2x. we put the x after our number to represent it as a gradient as the straight line formula is y = mx+c and you've found the m. NOW. use the formula Y-Y1=m(x-x1) to find the equation of the line.Again u can use any Y1 and X1 here but remember your m is 2
replace the digits and solve...Hopefully you'll get sth like this if you use the points (6,7): Y-7 = 2(x-6) .... y=2x-12+7... Y=2x-5! <<<< this is your straight line equation! Now all u gotta do is rearrange all your options into y = mx+c. D. is incorrect as it gives us y=2x+5 and not y = 2x-5 unlike the others
![\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6]](https://tex.z-dn.net/?f=%5Cvec%7BBE%7D%3D%5B-2-%28-6%29%3B%5C%204-10%5D%3D%5B4%3B%5C%20-6%5D)
![D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}](https://tex.z-dn.net/?f=D%28x%3B%5C%20y%29%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Bx-%28-2%29%3B%5C%20y-4%5D%3D%5Bx%2B2%3B%5C%20y-4%5D%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Cvec%7BBE%7D%5C%20therefore%5C%5C%5C%5C%20%5C%20%5Bx%2B2%3B%5C%20y-4%5D%3D%5B4%3B%5C%20-6%5D%5Cto%20x%2B2%3D4%5C%20and%5C%20y-4%3D-6%5C%5C%5C%5Cx%3D2%5C%20and%5C%20y%3D-2%5C%5C%5C%5CAnswer%3A%5C%20%5Cboxed%7BA.%5C%20%282%3B%5C%20-2%29%7D)
