❓ Question
Draw the graphs of the equations
and
Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
đź–Ľ️ Solution Image
✍️ Short Concept
This question is based on:
👉 Graph of Linear Equations
👉 Finding Intersection Points
👉 Coordinates of Vertices of a Triangle
đź”· Step 1 — Draw the First Line
Given:
Finding two points:
| x | y |
|---|---|
| 0 | 1 |
| -1 | 0 |
Thus the line passes through:
đź”· Step 2 — Draw the Second Line
Given:
Finding two points:
| x | y |
|---|---|
| 0 | 6 |
| 4 | 0 |
Thus the line passes through:
đź”· Step 3 — Find the Point of Intersection
From
Substitute into
Putting in
Therefore, intersection point is
đź”· Step 4 — Find the Vertices of the Triangle
The triangle is formed by the two lines and the x-axis.
Vertex A (Intersection of lines)
Vertex B (x-intercept of first line)
Vertex C (x-intercept of second line)
✅ Final Answer
The vertices of the triangle are:
🚨 Common Mistakes
❌ Taking y-intercepts instead of x-intercepts as triangle vertices
❌ Arithmetic mistake while solving for intersection point
❌ Forgetting that the triangle is formed with the x-axis
✅ Final Takeaway
To find the triangle formed by two lines and the x-axis:
✔ Find x-intercepts of both lines
✔ Find the intersection point of the lines
✔ These three points become the vertices of the triangle
Thus, the required vertices are: