Question

Standardized Test Practice What is the perimeter of

triangle DEF if its vertices are D(-2, -6), E(-2, 6) and
F(3, -6)?
A 12 units
B
13 units
C 17 units
D
30 units

Answer 1

To find the perimeter of triangle DEF with vertices D(-2, -6), E(-2, 6), and F(3, -6), we calculate the three sides using the distance formula and add them up. The perimeter is 12 units + 5 units + 13 units, which totals 30 units.

Step-by-step explanation:

The perimeter of triangle DEF can be determined by calculating the distances between the given vertices D(-2, -6), E(-2, 6), and F(3, -6). To find the distance between two points, we use the distance formula √((x2-x1)² + (y2-y1)²). Applying this formula:

• Distance DE = √((-2 + 2)² + (6 - (-6))²) = √(0² + 12²) = 12 units
• Distance DF = √((3 - (-2))² + (-6 - (-6))²) = √(5² + 0²) = 5 units
• Distance EF = √((3 - (-2))² + (-6 - 6)²) = √(5² + (-12)²) = 13 units

Adding these distances gives us the perimeter of the triangle:

Perimeter = DE + DF + EF = 12 units + 5 units + 13 units = 30 units

Therefore, the correct answer is D, 30 units.