Find the area of a triangle having vertices A(3, 2), B(1, 8), and C(8, 12).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Find the area of a triangle having vertices \( A(3, 2) \), \( B(1, 8) \), and \( C(8, 12) \).
---
To find the area of a triangle given its vertices, use the formula for the area \( A \) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ A = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
By plugging in the coordinates of vertices \( A(3, 2) \), \( B(1, 8) \), and \( C(8, 12) \), the formula becomes:
\[ A = \frac{1}{2} \left| 3(8-12) + 1(12-2) + 8(2-8) \right| \]
\[ A = \frac{1}{2} \left| 3(-4) + 1(10) + 8(-6) \right| \]
\[ A = \frac{1}{2} \left| -12 + 10 - 48 \right| \]
\[ A = \frac{1}{2} \left| -50 \right| \]
\[ A = \frac{1}{2} \times 50 \]
\[ A = 25 \]
Thus, the area of the triangle is \( 25 \) square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4f4865a-ef7d-48b6-9e5b-0e85084b2d7c%2F63462b97-ec6f-49ce-9b05-382327c88958%2Fmru1of_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the area of a triangle having vertices \( A(3, 2) \), \( B(1, 8) \), and \( C(8, 12) \).
---
To find the area of a triangle given its vertices, use the formula for the area \( A \) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ A = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
By plugging in the coordinates of vertices \( A(3, 2) \), \( B(1, 8) \), and \( C(8, 12) \), the formula becomes:
\[ A = \frac{1}{2} \left| 3(8-12) + 1(12-2) + 8(2-8) \right| \]
\[ A = \frac{1}{2} \left| 3(-4) + 1(10) + 8(-6) \right| \]
\[ A = \frac{1}{2} \left| -12 + 10 - 48 \right| \]
\[ A = \frac{1}{2} \left| -50 \right| \]
\[ A = \frac{1}{2} \times 50 \]
\[ A = 25 \]
Thus, the area of the triangle is \( 25 \) square units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
