Question

Q8 The equation of two sides of a square are 3x + 4y - 5 =0 and 3x + 4y - 15 = 0 and (6,5) is a point on
the third side. Find the equation of the third side and the remaining side.
(4x – 3y - 9 =0 and 4x – 3y -19 =0)​

Answer 1

Answer:

Step-by-step explanation:

The other two sides will have equations of the form 4x – 3y + k = 0.

Since one of them passes through (6,5) we get one value of k as -9, and therefore, one of the remaining sides as 4x – 3y – 9 = 0.

Since the equations represent sides of a square, the distance between the opposite sides will be equal.

That is, the distance between 3x + 4y – 5 = 0 and 3x + 4y – 15 = 0 will be same as the distance between 4x – 3y – 9 = 0 and the fourth side 4x – 3y + k = 0.

Hence we get the relation, |(-5)-(-15)|/√3²+4² = |-9-k|/√4²+(−3)², or |k+9|=10

This gives two values of k, 1 and -19, and therefore, two possible equations of the fourth side 4x – 3y + 1 = 0 and 4x – 3y – 19 = 0.