To determine the correct sketch for the point [tex]\( (2 \sqrt{5}, -4) \)[/tex], let's follow these steps:
1. Understand the Point Coordinates:
- The point is given as [tex]\( (2 \sqrt{5}, -4) \)[/tex].
- [tex]\( 2 \sqrt{5} \)[/tex] is the x-coordinate.
- [tex]\( -4 \)[/tex] is the y-coordinate.
2. Approximate the Value of [tex]\( 2 \sqrt{5} \)[/tex]:
- The numerical value of [tex]\( 2 \sqrt{5} \)[/tex] is approximately [tex]\( 4.472 \)[/tex].
3. Plot the Point on a Cartesian Plane:
- The x-coordinate is approximately [tex]\( 4.472 \)[/tex], which means the point is a little less than halfway between 4 and 5 on the x-axis.
- The y-coordinate is [tex]\( -4 \)[/tex], which means you would move 4 units down from the origin on the y-axis.
4. Locate the Point on the Graph:
- Start at the origin (0, 0).
- Move horizontally to the right to approximately 4.472 on the x-axis.
- From there, move vertically downwards to -4 on the y-axis.
So, the correct sketch is the one that shows a point located slightly less than halfway between 4 and 5 on the x-axis and exactly 4 units below the x-axis on the y-axis.
Please refer to the Cartesian plane with these values to identify the correct sketch.
