wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.

Open in App
Solution

Let A(1, 2), C(5, 8), B(x1,y1), D(x2,y2)

Slope of AC =8251=64=32

Let m be the slope of a line making an angle 45 with AC.

tan 45=m1321+m×32

1=m321+3m2

1+3m2=m32 or, 1+3m2=(m32)

3m2m=321 or, 1+3m2=m+32

12m=52 or, 3m2+m=321

m=5 or, 5m2=12

m=15

Consider the following figure:

Hence, equation of AD.

y2=5(x1)

y2=5x+5

5x+y=7

Equation of CD,

y8=15(x5)

y8=x51y8=x55

=5y40=x55yx=35

x5y+35=0

Hence co-ordinates are (6, 3), (0, 7)

The equation of AB is

y2=15(x1)

5y10=x1

x5y+9=0

And the equation of BC is

y8=5(x5)

y8=5x+25

5x+y33=0


flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Straight Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon