Question

2.2 practice
plot each point.

1. k(-3,1) j(-4,-4) i(2,3) h(4,-1) g(-2,0)
2. n(0,2) m(-5,0) l(5,5) k(-4,-4) j(-3,3)
3. e(3,-1) f(1,-1) g(4,-4) h(-3,0) i(4,2)
4. i(2,1) h(5,0) g(1,-4) f(-1,-1) e(-1,2)

state the quadrant or axis that each point lies in.

1. d(3,-2) e(-2,5) f(4,4)
2. i(5,2) h(-3,-5) g(3,0)

Explanation:

Step1: Recall quadrant rules

In a Cartesian coordinate system, points \((x,y)\) with \(x>0,y > 0\) are in the first quadrant; \(x<0,y>0\) in the second quadrant; \(x < 0,y<0\) in the third quadrant; \(x>0,y<0\) in the fourth quadrant. Points on the \(x\) - axis have \(y = 0\) and points on the \(y\) - axis have \(x = 0\).

Step2: Analyze each point

For example, for the point \(K(-3,1)\), since \(x=-3<0\) and \(y = 1>0\), it lies in the second quadrant. Repeat this process for all given points.

Answer:

1.

• For \(K(-3,1)\): Second - quadrant
• For \(J(-4, - 4)\): Third - quadrant
• For \(I(2,3)\): First - quadrant
• For \(H(4,-1)\): Fourth - quadrant
• For \(G(-2,0)\): \(x\) - axis

2.

• For \(N(0,2)\): \(y\) - axis
• For \(M(-5,0)\): \(x\) - axis
• For \(L(5,5)\): First - quadrant
• For \(K(-4,-4)\): Third - quadrant
• For \(J(-3,3)\): Second - quadrant

3.

• For \(E(3,-1)\): Fourth - quadrant
• For \(F(1,-1)\): Fourth - quadrant
• For \(G(4,-4)\): Fourth - quadrant
• For \(H(-3,0)\): \(x\) - axis
• For \(I(4,2)\): First - quadrant

4.

• For \(I(2,1)\): First - quadrant
• For \(H(5,0)\): \(x\) - axis
• For \(G(1,-4)\): Fourth - quadrant
• For \(F(-1,-1)\): Third - quadrant
• For \(E(-1,2)\): Second - quadrant

5.

• For \(D(3,-2)\): Fourth - quadrant
• For \(E(-2,5)\): Second - quadrant
• For \(F(4,4)\): First - quadrant

6.

• For \(I(5,2)\): First - quadrant
• For \(H(-3,-5)\): Third - quadrant
• For \(G(3,0)\): \(x\) - axis