Question

answer attempt 1 out of 2 leg 1: leg 2: distance: submit answer

Explanation:

Step1: Identify coordinates of points

Let's assume the two yellow points are \((2, -6)\) and \((6, 3)\) (by looking at the grid: first point has \(x = 2\), \(y=-6\); second has \(x = 6\), \(y = 3\)).

Step2: Calculate Leg 1 (horizontal distance)

Horizontal distance is difference in \(x\)-coordinates: \(|6 - 2|=4\)

Step3: Calculate Leg 2 (vertical distance)

Vertical distance is difference in \(y\)-coordinates: \(|3 - (-6)|=|3 + 6| = 9\)

Step4: Calculate Distance (using Pythagorean theorem)

Distance \(d=\sqrt{(\text{Leg 1})^2+(\text{Leg 2})^2}=\sqrt{4^2 + 9^2}=\sqrt{16 + 81}=\sqrt{97}\approx9.85\) (but let's check coordinates again. Wait, maybe the points are \((2, -6)\) and \((6, 3)\)? Wait, another way: maybe the horizontal leg is from \(x = 2\) to \(x = 6\), so \(6 - 2 = 4\)? No, wait, looking at the grid, the first yellow dot: let's see, the \(x\)-axis: the first dot (lower one) is at \(x = 2\) (since from origin, 2 units right), \(y=-6\) (6 units down). The upper dot: \(x = 6\)? Wait, no, the vertical dashed line is at \(x = 6\)? Wait, the horizontal dashed line is from \(x = 2\) to \(x = 6\), so length is \(6 - 2 = 4\)? No, wait, the vertical leg: from \(y=-6\) to \(y = 3\), so \(3 - (-6)=9\). Wait, maybe the points are \((2, -6)\) and \((6, 3)\). Then Leg 1 (horizontal) is \(6 - 2 = 4\)? No, wait, maybe the horizontal leg is \(6 - 2 = 4\)? Wait, no, let's check the grid again. Wait, the lower yellow dot: \(x = 2\), \(y=-6\). The upper yellow dot: \(x = 6\), \(y = 3\)? Wait, no, the vertical dashed line is at \(x = 6\), and horizontal dashed line at \(y=-6\). So the horizontal leg is \(6 - 2 = 4\)? Wait, no, \(x\) from 2 to 6: difference is 4. Vertical leg: \(y\) from -6 to 3: difference is \(3 - (-6)=9\). Then distance is \(\sqrt{4^2 + 9^2}=\sqrt{16 + 81}=\sqrt{97}\approx9.85\). Wait, but maybe the points are \((2, -6)\) and \((6, 3)\). Wait, another possibility: maybe the horizontal leg is \(6 - 2 = 4\)? No, wait, let's re-express.

Wait, maybe the two points are \((2, -6)\) and \((6, 3)\). So:

Leg 1 (horizontal): \(|6 - 2| = 4\)

Leg 2 (vertical): \(|3 - (-6)| = 9\)

Distance: \(\sqrt{4^2 + 9^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.85\)

But maybe I made a mistake in coordinates. Wait, the lower yellow dot: let's count the grid. From origin (0,0), moving right 2 units (x=2), down 6 units (y=-6). The upper yellow dot: right 6 units (x=6), up 3 units (y=3). So horizontal difference: 6 - 2 = 4. Vertical difference: 3 - (-6) = 9. So Leg 1: 4, Leg 2: 9, Distance: \(\sqrt{4^2 + 9^2} = \sqrt{97}\).

Answer:

Leg 1: \(4\), Leg 2: \(9\), Distance: \(\sqrt{97}\) (or approximately \(9.85\))