Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th

# The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex. - Mathematics

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The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.

#### Solution

Let the vertices A(2, 1), B(3, –2) and C(x, y)

Area of a triangle = 5 sq. units

1/2[x_1y_2 + x_2y_3 + x_3y_1 - (x_2y_1 + x_3y_2 + x_1y_3)] = 5

1/2[- 4 + 3y + x - (3 - 2x + 2y)] = 5

– 4 + 3y + x – 3 + 2x – 2y = 10

3x + y – 7 = 10

3x + y = 17  ...(1)

Given y = x + 3

Substitute the value ofy = x + 3 in (1)

3x + x + 3 = 17

4x = 17 – 3

4x = 14

x = 14/4 = 7/2

Substitute the value of x in y = x + 3

y = 7/2 + 3

⇒ y = (7 + 6)/2

= 13/2

∴ The coordinates of the third vertex is (7/2, 13/2)

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#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 5 Coordinate Geometry
Unit Exercise – 5 | Q 2 | Page 237