Question
Point I lies on GH such that GI:HI is 3:1 Graph I
Answers
GPT-4o mini
To represent the point I on the segment GH such that the ratio GI:HI is 3:1, you can follow these steps:
1. **Identify Points G and H**: Start by defining the coordinates of points G and H. Let's assume G is at the coordinate (0, 0) and H is at (4, 0) for simplicity. This allows us to place point I on the line segment GH.
2. **Calculate the Distance**: The distance between G and H is calculated as follows:
\[
\text{Distance} (GH) = 4 - 0 = 4 \text{ units}
\]
3. **Divide the Segment Based on the Ratio**: Since the ratio GI:HI is 3:1, you can think of the entire segment GH as being divided into 4 equal parts (3 parts for GI and 1 part for HI).
- Length of GI = \( \frac{3}{4} \times 4 = 3 \) units
- Length of HI = \( \frac{1}{4} \times 4 = 1 \) unit
4. **Find the Location of Point I**:
- Starting from point G (0, 0), moving 3 units to the right will place point I at:
\[
I = (0 + 3, 0) = (3, 0)
\]
5. **Graphing Points**: You can now graph points G (0, 0), H (4, 0), and I (3, 0) on a Cartesian plane.
Your graph would have point G at the origin (0, 0), point H at (4, 0), and point I at (3, 0), clearly showing the ratio of the segments.
This graphical representation illustrates how point I divides line segment GH in the ratio of 3:1.
1. **Identify Points G and H**: Start by defining the coordinates of points G and H. Let's assume G is at the coordinate (0, 0) and H is at (4, 0) for simplicity. This allows us to place point I on the line segment GH.
2. **Calculate the Distance**: The distance between G and H is calculated as follows:
\[
\text{Distance} (GH) = 4 - 0 = 4 \text{ units}
\]
3. **Divide the Segment Based on the Ratio**: Since the ratio GI:HI is 3:1, you can think of the entire segment GH as being divided into 4 equal parts (3 parts for GI and 1 part for HI).
- Length of GI = \( \frac{3}{4} \times 4 = 3 \) units
- Length of HI = \( \frac{1}{4} \times 4 = 1 \) unit
4. **Find the Location of Point I**:
- Starting from point G (0, 0), moving 3 units to the right will place point I at:
\[
I = (0 + 3, 0) = (3, 0)
\]
5. **Graphing Points**: You can now graph points G (0, 0), H (4, 0), and I (3, 0) on a Cartesian plane.
Your graph would have point G at the origin (0, 0), point H at (4, 0), and point I at (3, 0), clearly showing the ratio of the segments.
This graphical representation illustrates how point I divides line segment GH in the ratio of 3:1.