Question

Find coordinates for a point that is three times as far from the origin as (2, 3) is. Describe the configuration of all such points.

a) (6, 9); Points form a straight line
b) (8, 12); Points form an equilateral triangle
c) (-6, -9); Points form a circle
d) (0, 0); Points are collinear

Answer 1

To find a point that is three times as far from the origin as (2, 3) is, multiply the coordinates of (2, 3) by 3. The coordinates of the new point are (6, 9). The configuration of all such points is a straight line.

Step-by-step explanation:

The point (2, 3) is three units away from the origin. To find a point that is three times as far from the origin, we multiply the coordinates of (2, 3) by 3. Therefore, the coordinates of the new point are (2*3, 3*3) which simplifies to (6, 9). The configuration of all such points is a straight line that passes through the origin and the point (6, 9).