Question

what are the coordinates of a point in quadrant i which is 5 units away from point q on the coordinate plane?

Explanation:

Step1: Determine coordinates of Q

From the graph, point Q is at \((-4, 1)\) (since x=-4, y=1).

Step2: Find point in Quadrant I

Quadrant I has positive x and y. We move 5 units from Q. Let's calculate the new coordinates. The x-coordinate of Q is -4. To move to Quadrant I (positive x), we can move 5 units right (since moving right increases x). So new x: \(-4 + 5 = 1\). The y-coordinate of Q is 1. To stay in Quadrant I (positive y), we can keep y positive. So the point is \((1, 1)\)? Wait, no, maybe using distance formula. Wait, the grid is 1 unit per square. Let's check the distance. From Q(-4,1), moving 5 units right: x becomes -4 +5=1, y remains 1? Wait, no, maybe the correct point is (1,1)? Wait, no, let's see. Wait, the distance from Q(-4,1) to (1,1) is 5 units (since 1 - (-4) =5, y same). And (1,1) is in Quadrant I (x>0, y>0).

Step3: Verify

Check coordinates: Q is (-4,1). The point (1,1) is 5 units to the right (since 1 - (-4) =5), and y=1. So it's 5 units away and in Quadrant I.

Answer:

\((1, 1)\)