Answer:
x = 5
Explanation:
Since all the sides of a square is equal then AB = BC
Given BC = 13 units and A is at (.x, 8) and B is at (-7,3)
To get AB, we will find the distance between the two coordinates as shown;
AB = √(x₂-x₁)²+(y₂-y₁)²
AB = √(-7-x)²+(3-8)²
Since AB = BC, then AB = 13
13 = √(-7-x)²+(3-8)²
square both sides
13² = (√(-7-x)²+(3-8)²)²
169 = (-7-x)²+(3-8)²
169 = 49+14x+x²+(-5)²
169 = 49+14x+x²+25
169 = x²+14x+74
x²+14x+74-169 = 0
x²+14x+74-169 = 0
x²+14x-95= 0
x²+19x-5x-95= 0
x(x+19)-5(x+19) = 0
x-5 = 0 and (x+19) = 0
x = 5 and x = -19
Since x> 0, hence the value of x is 5