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# The Area of a Triangle is 5 Sq Units. Two of Its Vertices Are (2, 1) and (3, –2). If the Third Vertex is (7/2, Y). Find the Value of Y - Mathematics

Answer in Brief

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (7/2, y). Find the value of y

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#### Solution

Let A(x_1,y_1) = A(2,1), B(x_2, y_2) = B(3,-2) and C(x_3,y_3) = C(7/2,y)

Now

Area(ΔABC) =1/2|x_1(y_2 - y_3) + x_2(y_3-y_1) + x_3(y_1 - y_2)|

=>5 = 1/2|2(-2-y) + 3(y - 1) + 7/2(1+2)|

=> 10 = |-4-2y+3y - 3 + 21/2|

=>10 = |y + 7/2|

=> 10 = y + 7/2 or -10 = y + 7/2

=> y = 13/2 or y = (-27)/2

Hence y = 13/2 or (-27)/2

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.5 | Q 22 | Page 54
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