Question

part a
indicate whether each point is located in quadrant i, quadrant ii, quadrant iii, quadrant iv, or none of the quadrants

point	quadrant i	quadrant ii	quadrant iii	quadrant iv	none
r(-2,-5)	○	○	○	○	○
s(-2,5)	○	○	○	○	○
t(2,-5)	○	○	○	○	○
v(0,5)	○	○	○	○	○

Explanation:

To solve this, we analyze each point based on the sign of its \(x\)- and \(y\)-coordinates:

Point \(P(2, 5)\)

• \(x = 2>0\), \(y = 5>0\)
• Quadrant I (both \(x,y\) positive)

Point \(R(-2, -5)\)

• \(x=-2 < 0\), \(y = -5<0\)
• Quadrant III (both \(x,y\) negative)

Point \(S(-2, 5)\)

• \(x=-2 < 0\), \(y = 5>0\)
• Quadrant II (\(x\) negative, \(y\) positive)

Point \(T(2, -5)\)

• \(x = 2>0\), \(y=-5 < 0\)
• Quadrant IV (\(x\) positive, \(y\) negative)

Point \(V(0, 5)\)

• \(x = 0\) (lies on the \(y\)-axis)
• None (not in any quadrant)

Resumen de las respuestas:

• \(P(2, 5)\): Cuadrante I
• \(R(-2, -5)\): Cuadrante III
• \(S(-2, 5)\): Cuadrante II
• \(T(2, -5)\): Cuadrante IV
• \(V(0, 5)\): Ninguno

(If you need to mark the circles, for each point, select the corresponding quadrant or "None" as per the above analysis.)

Answer:

To solve this, we analyze each point based on the sign of its \(x\)- and \(y\)-coordinates:

Point \(P(2, 5)\)

• \(x = 2>0\), \(y = 5>0\)
• Quadrant I (both \(x,y\) positive)

Point \(R(-2, -5)\)

• \(x=-2 < 0\), \(y = -5<0\)
• Quadrant III (both \(x,y\) negative)

Point \(S(-2, 5)\)

• \(x=-2 < 0\), \(y = 5>0\)
• Quadrant II (\(x\) negative, \(y\) positive)

Point \(T(2, -5)\)

• \(x = 2>0\), \(y=-5 < 0\)
• Quadrant IV (\(x\) positive, \(y\) negative)

Point \(V(0, 5)\)

• \(x = 0\) (lies on the \(y\)-axis)
• None (not in any quadrant)

Resumen de las respuestas:

• \(P(2, 5)\): Cuadrante I
• \(R(-2, -5)\): Cuadrante III
• \(S(-2, 5)\): Cuadrante II
• \(T(2, -5)\): Cuadrante IV
• \(V(0, 5)\): Ninguno

(If you need to mark the circles, for each point, select the corresponding quadrant or "None" as per the above analysis.)