Question

state the quadrant or axis that each point lies in.

1. ( l(-2,1) ) ( k(-3,-2) ) ( j(3,1) )
2. ( t(-3,5) ) ( u(1,0) ) ( v(-5,5) )
3. ( s(5,-7) ) ( t(7,2) ) ( u(-5,4) )
4. ( r(7,0) ) ( q(8,-1) ) ( p(3,0) )

Explanation:

Step1: Recall the quadrant rules

In a coordinate plane:

• Quadrant I: \(x>0,y>0\)
• Quadrant II: \(x < 0,y>0\)
• Quadrant III: \(x<0,y < 0\)
• Quadrant IV: \(x>0,y < 0\)
• \(x -\)axis: \(y = 0\)
• \(y -\)axis: \(x = 0\)

Step2: Analyze each point

For \(L(-2,1)\)

Here \(x=-2<0\) and \(y = 1>0\), so it lies in Quadrant II.

For \(K(-3,-2)\)

Here \(x=-3<0\) and \(y=-2<0\), so it lies in Quadrant III.

For \(J(3,1)\)

Here \(x = 3>0\) and \(y=1>0\), so it lies in Quadrant I.

For \(T(-3,5)\)

Here \(x=-3<0\) and \(y = 5>0\), so it lies in Quadrant II.

For \(U(1,0)\)

Here \(y = 0\), so it lies on the \(x -\)axis.

For \(V(-5,5)\)

Here \(x=-5<0\) and \(y = 5>0\), so it lies in Quadrant II.

For \(S(5,-7)\)

Here \(x = 5>0\) and \(y=-7<0\), so it lies in Quadrant IV.

For \(T(7,2)\)

Here \(x = 7>0\) and \(y=2>0\), so it lies in Quadrant I.

For \(U(-5,4)\)

Here \(x=-5<0\) and \(y = 4>0\), so it lies in Quadrant II.

For \(R(7,0)\)

Here \(y = 0\), so it lies on the \(x -\)axis.

For \(Q(8,-1)\)

Here \(x = 8>0\) and \(y=-1<0\), so it lies in Quadrant IV.

For \(P(3,0)\)

Here \(y = 0\), so it lies on the \(x -\)axis.

Answer:

1. \(L(-2,1)\) is in Quadrant II, \(K(-3,-2)\) is in Quadrant III, \(J(3,1)\) is in Quadrant I.
2. \(T(-3,5)\) is in Quadrant II, \(U(1,0)\) is on the \(x -\)axis, \(V(-5,5)\) is in Quadrant II.
3. \(S(5,-7)\) is in Quadrant IV, \(T(7,2)\) is in Quadrant I, \(U(-5,4)\) is in Quadrant II.
4. \(R(7,0)\) is on the \(x -\)axis, \(Q(8,-1)\) is in Quadrant IV, \(P(3,0)\) is on the \(x -\)axis.