Question

which is true about the point $(x, -5)$?
if $x = -3$, then the point is in the same quadrant as $(-5, -3)$.
if $x = 1$, then the point is in the same quadrant as $(0, -3)$.
if $x = 0$, then the point is in the same quadrant as $(0, 3)$.
if $x = 2$, then the point is in the same quadrant as $(-5, 2)$.

Explanation:

Step1: Determine quadrants of given points

• For \((-5,2)\): \(x=-5<0\), \(y = 2>0\), so it is in the second quadrant.
• For \((0,3)\): \(x = 0\), \(y=3>0\), so it is on the positive \(y -\)axis.
• For \((0,-3)\): \(x = 0\), \(y=-3<0\), so it is on the negative \(y -\)axis.
• For \((-5,-3)\): \(x=-5<0\), \(y=-3<0\), so it is in the third quadrant.

Step2: Analyze each option

• Option 1 (\(x = 2\)): The point is \((2,-5)\). Here \(x = 2>0\), \(y=-5<0\), so it is in the fourth quadrant. Different from \((-5,2)\) (second quadrant).
• Option 2 (\(x = 0\)): The point is \((0,-5)\). It is on the negative \(y -\)axis. Different from \((0,3)\) (positive \(y -\)axis).
• Option 3 (\(x = 1\)): The point is \((1,-5)\). Here \(x = 1>0\), \(y=-5<0\), so it is in the fourth quadrant. Different from \((0,-3)\) (negative \(y -\)axis).
• Option 4 (\(x=-3\)): The point is \((-3,-5)\). Here \(x=-3<0\), \(y =-5<0\), so it is in the third quadrant. Same as \((-5,-3)\) (third quadrant).

Answer:

If \(x=-3\), then the point is in the same quadrant as \((-5,-3)\).