To find the area of the triangle formed by the points P(0, 1), Q(0, 5), and R(3, 4), we can follow these steps:
### Step 1: Identify the coordinates of the points
The points are:
- P(0, 1)
- Q(0, 5)
- R(3, 4)
### Step 2: Plot the points on the coordinate plane
- Point P is located at (0, 1) on the y-axis.
- Point Q is located at (0, 5) on the y-axis.
- Point R is located at (3, 4) in the first quadrant.
### Step 3: Determine the base and height of the triangle
- The base of the triangle can be considered as the vertical line segment PQ, which lies on the y-axis.
- The length of the base (PQ) can be calculated as the difference in the y-coordinates of points Q and P:
\[
\text{Base} = Q_y - P_y = 5 - 1 = 4 \text{ units}
\]
- The height of the triangle can be determined by the horizontal distance from point R to the y-axis (the line x = 0). The x-coordinate of point R is 3, which gives us the height:
\[
\text{Height} = R_x = 3 \text{ units}
\]
### Step 4: Use the formula for the area of a triangle
The area \( A \) of a triangle is given by the formula:
\[
A = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Substituting the values we found:
\[
A = \frac{1}{2} \times 4 \times 3
\]
### Step 5: Calculate the area
Calculating the area:
\[
A = \frac{1}{2} \times 12 = 6 \text{ square units}
\]
### Final Answer
The area of the triangle formed by the points P(0, 1), Q(0, 5), and R(3, 4) is **6 square units**.
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