Question

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answer
leg 1: leg 2: hypotenuse:

Explanation:

Step1: Identify Coordinates

First, find the coordinates of the two points. Let's assume the first point (let's call it \( A \)) is at \( (-1, 9) \) and the second point ( \( B \)) is at \( (8, 6) \). Wait, maybe better to look at the horizontal and vertical distances. Wait, maybe the right triangle is formed by dropping vertical and horizontal lines. Let's check the horizontal distance (change in \( x \)) and vertical distance (change in \( y \)).

Wait, maybe the two points are \( ( -1, 9) \) and \( (8, 6) \). Then the horizontal leg (Leg 1) is the difference in \( x \)-coordinates: \( 8 - (-1) = 9 \)? Wait, no, maybe the grid. Wait, looking at the graph, the first point is at \( x=-1, y=9 \), the second at \( x=8, y=6 \). Wait, no, maybe the vertical leg is the difference in \( y \): \( 9 - 6 = 3 \), and horizontal leg is \( 8 - (-1) = 9 \)? Wait, no, maybe I misread. Wait, maybe the points are \( (0,9) \) and \( (8,6) \)? No, the first point is at \( x=-1 \) (since the x-axis has -1, 0, 1...). Wait, maybe the horizontal distance (Leg 1) is \( 8 - (-1) = 9 \)? No, that seems too big. Wait, maybe the points are \( (-1, 9) \) and \( (8, 6) \), so the horizontal change is \( 8 - (-1) = 9 \), vertical change is \( 9 - 6 = 3 \). Then Leg 1 (horizontal) is 9, Leg 2 (vertical) is 3? Wait, no, maybe the other way. Wait, maybe the two points are \( (-1, 9) \) and \( (8, 6) \), so the horizontal leg is \( 8 - (-1) = 9 \), vertical leg is \( 9 - 6 = 3 \). Then hypotenuse is \( \sqrt{9^2 + 3^2} = \sqrt{81 + 9} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). But that doesn't seem right. Wait, maybe I made a mistake. Wait, maybe the points are \( ( -1, 9) \) and \( (8, 6) \), but maybe the vertical leg is \( 9 - 6 = 3 \), horizontal leg is \( 8 - (-1) = 9 \). Then Leg 1: 9, Leg 2: 3, Hypotenuse: \( \sqrt{9^2 + 3^2} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). But maybe the points are different. Wait, maybe the first point is at \( ( -1, 9) \) and the second at \( (8, 6) \), so horizontal distance (Leg 1) is \( 8 - (-1) = 9 \), vertical distance (Leg 2) is \( 9 - 6 = 3 \). Then hypotenuse is \( \sqrt{9^2 + 3^2} = \sqrt{81 + 9} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). But maybe I misread the coordinates. Alternatively, maybe the points are \( (0,9) \) and \( (8,6) \), but the first point is at \( x=-1 \). Wait, maybe the grid is such that each square is 1 unit. So from \( x=-1 \) to \( x=8 \) is 9 units (horizontal), from \( y=6 \) to \( y=9 \) is 3 units (vertical). So Leg 1: 9, Leg 2: 3, Hypotenuse: \( \sqrt{9^2 + 3^2} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). But maybe the problem is to find the lengths of the legs and hypotenuse of the right triangle formed by the two points and the right angle at the intersection of the horizontal and vertical lines. So Leg 1 (horizontal) is \( 8 - (-1) = 9 \), Leg 2 (vertical) is \( 9 - 6 = 3 \), Hypotenuse is \( \sqrt{9^2 + 3^2} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). But maybe I made a mistake. Wait, maybe the points are \( (-1, 9) \) and \( (8, 6) \), so horizontal difference is \( 8 - (-1) = 9 \), vertical difference is \( 9 - 6 = 3 \). So Leg 1: 9, Leg 2: 3, Hypotenuse: \( \sqrt{9^2 + 3^2} = \sqrt{90} \approx 9.4868 \). But maybe the problem expects integer lengths. Wait, maybe I misread the coordinates. Let me check again. The first point is at \( x=-1 \), \( y=9 \) (since the y-axis has 9, 8, 7, 6...). The second point is at \( x=8 \), \( y=6 \). So the horizontal leg (Leg 1) is \( 8 - (-1) = 9 \), vertical leg (Leg 2) is \( 9 - 6 = 3 \). Then hypotenuse is \( \sqrt{9^2 + 3^2} = \sqrt{81 + 9} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \). So Leg 1: 9, Leg 2: 3, Hypotenuse: \( 3\sqrt{10} \) (or approximately 9.49).

Step2: Calculate Legs and Hypotenuse

Leg 1 (horizontal distance): \( |8 - (-1)| = 9 \)
Leg 2 (vertical distance): \( |9 - 6| = 3 \)
Hypotenuse: \( \sqrt{9^2 + 3^2} = \sqrt{81 + 9} = \sqrt{90} = 3\sqrt{10} \approx 9.4868 \)

Answer:

Leg 1: \( 9 \), Leg 2: \( 3 \), Hypotenuse: \( 3\sqrt{10} \) (or approximately \( 9.49 \))