Show that the points A(0,6), B(2,1) and C(7,3) are the three corners of a square ABCD Find i) the - Maths - Straight Lines

Question

Show that the points A(0,6), B(2,1) and C(7,3) are the three
corners of a square ABCD Find i) the slope of the diagonal BD and
ii) the coordinates of the fourth vertex D

Priyanka Kedia · Accepted Answer

Let the coordinates of the fourth vertex D be (x,y)
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_57b2eb4390b72%20png">

Mid point of diagonal AC=0+72,6+32=72,92Mid point of diagonal BD=2+x2,1+y2We know that, diagonals of square bisect each other
 So, Mid point of diagonal AC=Mid point of diagonal BD⇒72,92=2+x2,1+y2⇒2+x2=72    and    1+y2=92⇒x=5  and y=8Now,Slope of diagonal BD=1-82-5=73             Using formula, m=y2-y1x2-x1And, the coordinates of fourth vertex D=5,8

Show that the points A(0,6), B(2,1) and C(7,3) are the three corners of a square ABCD. Find i) the slope of the diagonal BD and ii) the coordinates of the fourth vertex D.