My Learning Cart
?
Categories
Account

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1,

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the area of the triangle?

Options:

  1. 6 square units
  2. 8 square units
  3. 10 square units
  4. 12 square units

Correct Answer: 6 square units

Solution: 

Using the formula Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|, we find Area = 1/2 |1(6 - 6) + 4(6 - 2) + 1(2 - 6)| = 1/2 |0 + 16 - 4| = 1/2 * 12 = 6 square units.

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1,

Practice Questions

Q1
If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the area of the triangle?
  1. 6 square units
  2. 8 square units
  3. 10 square units
  4. 12 square units

Questions & Step-by-Step Solutions

If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the area of the triangle?
  • Step 1: Identify the coordinates of the triangle's vertices. We have A(1, 2), B(4, 6), and C(1, 6).
  • Step 2: Write down the formula for the area of a triangle using coordinates: Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.
  • Step 3: Assign the coordinates to the variables in the formula: x1 = 1, y1 = 2, x2 = 4, y2 = 6, x3 = 1, y3 = 6.
  • Step 4: Substitute the values into the formula: Area = 1/2 |1(6 - 6) + 4(6 - 2) + 1(2 - 6)|.
  • Step 5: Calculate each part inside the absolute value: 1(6 - 6) = 1(0) = 0, 4(6 - 2) = 4(4) = 16, 1(2 - 6) = 1(-4) = -4.
  • Step 6: Combine the results: Area = 1/2 |0 + 16 - 4| = 1/2 |12|.
  • Step 7: Calculate the final area: Area = 1/2 * 12 = 6 square units.
  • Area of a Triangle Using Coordinates – The question tests the ability to calculate the area of a triangle given its vertex coordinates using the determinant formula.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks