Question
Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. (3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Drawing a straight line from the starting point to the ending point would create a Response area triangle.
You can use the Response area to find the direct straight line distance for Jimmy.
If Jimmy took the direct line, he would have traveled approximately Response area meters.
Skip to navigation
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Drawing a straight line from the starting point to the ending point would create a Response area triangle.
You can use the Response area to find the direct straight line distance for Jimmy.
If Jimmy took the direct line, he would have traveled approximately Response area meters.
Skip to navigation
Answers
GPT-4o mini
To solve the problem, we can visualize Jimmy's movements on a coordinate plane.
1. **Starting point (home)**: We can assume this is at the origin (0,0).
2. **First movement (20 meters west)**: This moves Jimmy to (-20, 0).
3. **Second movement (25 meters north)**: This moves Jimmy to (-20, 25).
Now, we need to find the straight-line distance from the starting point (0, 0) to his ending point (-20, 25).
We can use the distance formula, which is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Plugging in the coordinates of home (0,0) and Jimmy's final position (-20, 25):
\[
d = \sqrt{((-20) - 0)^2 + (25 - 0)^2}
\]
\[
d = \sqrt{(-20)^2 + (25)^2}
\]
\[
d = \sqrt{400 + 625}
\]
\[
d = \sqrt{1025}
\]
\[
d \approx 32.02 \text{ meters}
\]
Therefore, the responses to fill in would be:
1. **Drawing a straight line from the starting point to the ending point would create a** **right triangle.**
2. **If Jimmy took the direct line, he would have traveled approximately** **32.02** **meters.**
1. **Starting point (home)**: We can assume this is at the origin (0,0).
2. **First movement (20 meters west)**: This moves Jimmy to (-20, 0).
3. **Second movement (25 meters north)**: This moves Jimmy to (-20, 25).
Now, we need to find the straight-line distance from the starting point (0, 0) to his ending point (-20, 25).
We can use the distance formula, which is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Plugging in the coordinates of home (0,0) and Jimmy's final position (-20, 25):
\[
d = \sqrt{((-20) - 0)^2 + (25 - 0)^2}
\]
\[
d = \sqrt{(-20)^2 + (25)^2}
\]
\[
d = \sqrt{400 + 625}
\]
\[
d = \sqrt{1025}
\]
\[
d \approx 32.02 \text{ meters}
\]
Therefore, the responses to fill in would be:
1. **Drawing a straight line from the starting point to the ending point would create a** **right triangle.**
2. **If Jimmy took the direct line, he would have traveled approximately** **32.02** **meters.**