Answer:
The correct option is;
a. 1
Explanation:
Given that the origin (0, 0) is the corner of the square
The equation of one of the sides = 3·X + 4·Y + 5 = 0
Therefore, we have;
Y = -3/4·X - 5/4
Which gives the slope as -3/4 and the y-intercept as (0, -5/4)
The sloe of the perpendicular side from the origin to the given line is therefore = -(1/(3/4)) = 4/3
The y-intercept of the current particular perpendicular side = 0
The equation is therefore;
y = 4/3·x + 0
The coordinate of the point of intersection of the two sides of the square above is found by equating the two lines to each other as follows;
4/3·x = -3/4·X - 5/4
4/3·x + 3/4·X = -5/4
25/12·X = -5/4
X = -5/4×12/25 = -3/5
Y = 4/3·x = 4/3× (-3/5) =-4/5
The length of a side = √((-3, 5) - 0)² + ((-4, 5) - 0)² = √1 = 1
The area of a square = (Length of side) × (Length of side)
∴ The area of the square = 1 × 1 = 1
The area of the square = 1.