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 DE?"

Option 1: 6
Option 2: 5
Option 3: 4
Option 4: 3

Answer 1

Using the distance formula derived from the Pythagorean theorem, the length of side DE in the triangle with vertices D (3, -3) and E (0, 2) is approximately 5.83, which rounds to 5 units, making Option 2 the closest choice.

Step-by-step explanation:

The student asked for the length of the side DE in a triangle with vertices D (3, -3), E (0, 2), and F (-1, -3). To find this length, we apply the distance formula which is derived from the Pythagorean theorem. The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of two points.

Therefore, for DE we have:

Distance = √((0-3)² + (2-(-3))²)
= √((-3)² + (5)²)
= √(9 + 25)
= √34
= 5.83095189...

The closest option to our calculated length is Option 2: 5 units, as we typically round to the nearest whole number for such calculations.