Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The area of a quadrilateral whose vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
48 sq.units
30 sq.units
24 sq.units
12 sq.units
24 sq.units
Use the shoelace method by writing coordinates in a column and cross-multiplying; sum the products downward and subtract the sum of products upward, then divide by 2.
Coordinates of quadrilateral vertices are (3, 0), (4, 5), (-1, 4), and (-2, -1).
Area=21∣(x1y2+x2y3+x3y4+x4y1)−(y1x2+y2x3+y3x4+y4x1)∣
Use the shoelace method by writing coordinates in a column and cross-multiplying; sum the products downward and subtract the sum of products upward, then divide by 2.
Students often forget to take the absolute value of the final result or misalign the coordinates when performing the cyclic multiplication.
Set up coordinates
List the vertices in cyclic order: (3,0),(4,5),(−1,4),(−2,−1) and repeat the first vertex.
(x1,y1)=(3,0),(x2,y2)=(4,5),(x3,y3)=(−1,4),(x4,y4)=(−2,−1)
Calculate downward sum
Calculate the sum of xi×yi+1 products: (3×5)+(4×4)+(−1×−1)+(−2×0).
Sum1=15+16+1+0=32
Calculate upward sum
Calculate the sum of yi×xi+1 products: (0×4)+(5×−1)+(4×−2)+(−1×3).
Sum2=0−5−8−3=−16
Final calculation
Apply the shoelace formula: Area=21∣Sum1−Sum2∣.
Area=21∣32−(−16)∣=21∣48∣=24
C is correct because the area calculated using the coordinate geometry determinant formula results in 24 sq.units.
The shoelace formula is a specialized application of the cross product of vectors, which is also fundamental in 3D geometry and Physics problems involving flux or torque.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants