Final answer:
To find the perimeter of square JKLM, calculate the distance between J and M using the distance formula and multiply by 4. This gives the perimeter as 8√5, which approximates to 17.9 units.
Step-by-step explanation:
The question involves finding the perimeter of a square on a coordinate plane, given two adjacent vertices.
We first need to calculate the length of one side using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates.
The formula is d = √((x2 - x1)² + (y2 - y1)²).
Given points J(-2,5) and M(-6,3), we substitute into the distance formula to get:
d = √((-6 - (-2))² + (3 - 5)²)
= √((-4)² + (-2)²)
= √(16 + 4)
= √20
Since the square has four sides of equal length, the perimeter is given by P = 4 * d. Hence:
P = 4 * √20
To express this as a whole number, decimal, or simplified radical, we simplify √20:
√20 = 2√5
Thus, the perimeter is:
P = 4 * (2√5)
= 8√5
Now we approximate √5 to 2.236:
P ≈ 4 * 2 * 2.236 = 4 * 4.472 = 17.888
The perimeter is approximately 17.9 units (rounded to one decimal place).
"Your question is incomplete, probably the complete question/missing part is:"
On the coordinate plane, J(-2,5) and M(-6,3) form one side of the square JKLM. Find the perimeter of JKLM. Write your answer as a whole number, decimal, or simplified radical.