Question

Area of the triangle whose vertices are (3,4),(4,5)and (2,-3)

a) 1 sq. unit
b) 5 sq. unit
c) 3 sq. unit
d) 2 sq. unit​

Answer 1

Given: Coordinates of a triangle are (3, 4), (4, 5) and (2, -3)

To find: The area of the triangle formed by the given coordinates.

Solution:

Whenever we are given three coordinates of a triangle and we are asked to find the area of this triangle, we may use the following formula:

• $\boxed{ \sf Area = \dfrac12 \bigg| x_1(y_2 - y_3) +x _2(y_3 - y_1) + x_3(y_1 - y_2)\bigg| }$

Let the given coordinates be:

• (x1, y1) = (3, 4)
• (x2, y2) = (4, 5)
• (x3, y3) = (2, -3)

Therefore the area is given by:

${ \sf\implies Area = \dfrac12 \bigg| x_1(y_2 - y_3) +x _2(y_3 - y_1) + x_3(y_1 - y_2)\bigg| }$

${ \sf\implies Area = \dfrac12 \bigg| 3(5 - ( - 3)) +4( - 3 - 4) + 2(4 - 5)\bigg| }$

${ \sf\implies Area = \dfrac12 \bigg| 3(8) +4( -7) + 2( - 1)\bigg| }$

${ \sf\implies Area = \dfrac12 \bigg| 24 - 28 - 2\bigg| }$

${ \sf\implies Area = \dfrac12 \bigg| - 6\bigg| }$

${ \sf\implies Area = \dfrac12(6)}$

$\purple{\boxed{ \sf\implies Area = 3}}$

Therefore the area of triangle is 3 sq. units.

Option (C) is correct.