Question

Draw a triangle with the following vertices on a coordinate plane. Show your drawing and label the vertices with the given ordered pairs. A(0,2) B(2,5) C(-1,7)

Answer 1

The triangle is located in the first quadrant of the coordinate plane, as all three vertices have positive x- and y-coordinates.

Vertex A lies on the x-axis, which means its y-coordinate is 0. Vertex B lies 2 units to the right of the origin and 3 units above the origin, giving it coordinates (2,5). Vertex C lies 1 unit to the left of the origin and 7 units above the origin, giving it coordinates (-1,7).

The lengths of the sides of the triangle can be determined using the distance formula:

`d^2 = (x2 - x1)^2 + (y2- y1)^2`

where d is the distance between the two points (x1, y1) and (x2, y2).

Side AB: d = (2 - 0)² + (5 - 2)² = √29

Side BC: d = (-1 - 2)² + (7 - 5)² = √15

Side AC: d = (-1 - 0)² + (7 - 2)² = √29

The lengths of all three sides are equal, which means the triangle is an equilateral triangle. An equilateral triangle is a triangle with all three sides equal and all three angles equal to 60 degrees.