To determine which quadrant each point lies in, we first need to understand the coordinate plane, also known as the Cartesian plane. The plane is divided into four quadrants, each defined by the signs of the x (horizontal) and y (vertical) coordinates of a point:
1. Quadrant I: [tex]\(x > 0\)[/tex] and [tex]\(y > 0\)[/tex]
2. Quadrant II: [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex]
3. Quadrant III: [tex]\(x < 0\)[/tex] and [tex]\(y < 0\)[/tex]
4. Quadrant IV: [tex]\(x > 0\)[/tex] and [tex]\(y < 0\)[/tex]
Now, let's determine the quadrant for each given point:
1. Point (2, 3):
- [tex]\(x = 2\)[/tex] which is greater than 0.
- [tex]\(y = 3\)[/tex] which is greater than 0.
- Therefore, (2, 3) lies in Quadrant I.
2. Point (-3, 4):
- [tex]\(x = -3\)[/tex] which is less than 0.
- [tex]\(y = 4\)[/tex] which is greater than 0.
- Therefore, (-3, 4) lies in Quadrant II.
3. Point (-3, -10):
- [tex]\(x = -3\)[/tex] which is less than 0.
- [tex]\(y = -10\)[/tex] which is less than 0.
- Therefore, (-3, -10) lies in Quadrant III.
In summary, the quadrants for the given points are:
(i) [tex]\((2,3)\)[/tex] : Quadrant I
(ii) [tex]\((-3,4)\)[/tex] : Quadrant II
(iii) [tex]\((-3,-10)\)[/tex] : Quadrant III
