Question

click twice to draw a line. click a segment to erase it.
answer attempt 1 out of 2
leg 1:
leg 2:
hypotenuse:
submit answer

Explanation:

Step1: Identify Coordinates

First, find the coordinates of the two yellow points. The upper point: let's assume the grid has integer coordinates. From the graph, the upper yellow point seems to be at \((3, 8)\) (wait, no, looking at the x-axis, the vertical dashed line is at x=3? Wait, the lower yellow point: let's check. The lower yellow point: x=-2, y=-4? Wait, maybe better to find the horizontal and vertical distances. Wait, the right triangle: one leg is horizontal, one vertical. Wait, the vertical leg: from (0,1) to (3,8)? No, maybe the two legs are the horizontal and vertical distances between the two points. Wait, let's take the two endpoints of the legs. Wait, the lower yellow point: let's say its coordinates are \((-2, -4)\) and the upper yellow point is \((3, 8)\)? No, maybe the right angle is at (3, -4) or something. Wait, maybe the horizontal leg (Leg 1) is the difference in x-coordinates, and vertical leg (Leg 2) is difference in y-coordinates. Wait, let's find the two points: let's say the lower point is \((-2, -4)\) and the upper point is \((3, 8)\)? No, maybe the right angle is at (3, -4). Wait, the vertical dashed line is at x=3, and the horizontal dashed line is at y=-4. So the right angle is at (3, -4). Then the lower yellow point is \((-2, -4)\) (so horizontal distance from x=-2 to x=3: that's \(3 - (-2) = 5\)? Wait, no, x from -2 to 3: difference is 5? Wait, the upper yellow point: from (3, -4) to (3, 8)? Wait, y from -4 to 8: difference is \(8 - (-4) = 12\)? No, that can't be. Wait, maybe I misread. Wait, the starting point is (0,1)? No, the graph has a point at (0,1) connected with dashed lines. Wait, maybe the two legs are: one leg is the horizontal distance between the two points (x-direction) and one leg is vertical distance (y-direction). Let's find the coordinates of the two yellow points. Let's assume the lower yellow point is \((-2, -4)\) and the upper yellow point is \((3, 8)\). Wait, no, the vertical dashed line is at x=3, and the horizontal dashed line is at y=-4. So the right angle is at (3, -4). Then the lower yellow point is \((-2, -4)\) (so horizontal leg: from x=-2 to x=3, length \(3 - (-2) = 5\)? Wait, no, absolute value: \(|3 - (-2)| = 5\)? Wait, no, 3 - (-2) is 5, so length 5. Then the vertical leg: from y=-4 to y=8? Wait, 8 - (-4) = 12? No, that's too long. Wait, maybe the upper yellow point is (3, 8)? No, the y-axis at 8? Wait, the grid: each square is 1 unit. Let's count the horizontal distance: from x=-2 to x=3: that's 5 units (since -2 to 0 is 2, 0 to 3 is 3, total 5). Vertical distance: from y=-4 to y=8? No, that's 12. But maybe the upper point is (3, 8) and lower is (-2, -4). Then Leg 1 (horizontal): 5, Leg 2 (vertical): 12? Wait, but then hypotenuse would be \(\sqrt{5^2 + 12^2} = 13\). Wait, but maybe I made a mistake. Wait, another approach: the two legs are the horizontal and vertical sides. Let's check the coordinates again. Let's say the lower yellow point is \((-2, -4)\) and the upper yellow point is \((3, 8)\). Then the horizontal distance (Leg 1) is \(3 - (-2) = 5\) (since x-coordinates: -2 to 3, difference 5). The vertical distance (Leg 2) is \(8 - (-4) = 12\) (y-coordinates: -4 to 8, difference 12). Then hypotenuse is \(\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13\). Wait, but maybe the legs are 5 and 12, hypotenuse 13. Alternatively, maybe the legs are 6 and 8? Wait, no, let's re-examine the graph. Wait, the vertical dashed line is at x=3, and the horizontal dashed line is at y=-4. The lower yellow point is at x=-2, y=-4 (so ( -2, -4)), and the upper yellow point is at x=3, y=8 (so (3, 8)). So the horizontal leg (Leg 1) is the distance between x=-2 and x=3: \(|3 - (-2)| = 5\). The vertical leg (Leg 2) is the distance between y=-4 and y=8: \(|8 - (-4)| = 12\). Then hypotenuse is \(\sqrt{5^2 + 12^2} = 13\). Wait, but maybe I messed up the coordinates. Wait, another way: the point at (0,1) is connected, but maybe the right triangle is formed by ( -2, -4), (3, -4), and (3, 8). Ah! Yes, that makes a right triangle. So ( -2, -4) to (3, -4) is horizontal leg: length \(3 - (-2) = 5\) (since y is same, -4). Then (3, -4) to (3, 8) is vertical leg: length \(8 - (-4) = 12\) (x same, 3). Then hypotenuse is from ( -2, -4) to (3, 8): \(\sqrt{5^2 + 12^2} = 13\). So Leg 1: 5, Leg 2: 12, Hypotenuse: 13.

Step2: Calculate Leg Lengths

Leg 1 (horizontal): distance between \((-2, -4)\) and \((3, -4)\) is \(|3 - (-2)| = 5\).
Leg 2 (vertical): distance between \((3, -4)\) and \((3, 8)\) is \(|8 - (-4)| = 12\).

Step3: Calculate Hypotenuse

Using Pythagorean theorem: \(c = \sqrt{a^2 + b^2}\), where \(a = 5\), \(b = 12\). So \(c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13\).

Answer:

Leg 1: \(\boldsymbol{5}\)
Leg 2: \(\boldsymbol{12}\)
Hypotenuse: \(\boldsymbol{13}\)