Question

A triangle has vertices on the coordinate grid at points D (3, -3), E (0, 2), and F (-1, -3). What is the length, in units, of DF ?

Answer 1

The length of DF, calculated using the distance formula based on the coordinates of points D (3, -3) and F (-1, -3), is 4 units.

Step-by-step explanation:

To calculate the length of DF in the triangle with vertices at D (3, -3), E (0, 2), and F (-1, -3), we use the distance formula which is derived from the Pythagorean theorem. The distance formula for two points in a coordinate plane is:

Distance = √((x2 - x1)² + (y2 - y1)²)

For points D and F, we plug in their coordinates (x1 = 3, y1 = -3) and (x2 = -1, y2 = -3) respectively:

DF = √((-1 - 3)² + (-3 - (-3))²)

DF = √((-4)² + (0)²)

DF = √(16 + 0)

DF = √(16)

DF = 4 units

The length of DF is 4 units.