Question

For what value of n the area of the triangle formed with points (1, n), (3,5) and (-1, 2) will be 5 sq units?


-1
2
1
None of these​

Answer 1

Step-by-step explanation:

⤴️

n=1 is correct answer.

hope this helps you mate ✨

Answer 2

Concept

The formula to calculate the area of a triangle which has (x1, y1), (x2, y2) and (x3, y3) as vertices is

Area = 1/2 * [ x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

Given

The three points of vertices is given as

(x1, y1) = (1, n)

(x2, y2) = (3, 5)

(x3, y3) = (-1, 2)

Area = 5 square unit

Find

We have to calculate the area and then find out the value of n.

Solution

Since, Area = 1/2 * [ x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

Therefore substituting the values from the given data to calculate the value of n, we have

Area = 1/2 * [ 1(5-2) + 3(2-n) -1(n-5)]

5 = 1/2 * [ 3 + 6 - 3n -n + 5]

10 = 14 - 4n

4n = 4

n = 1

Hence the calculated value of n for the area of the triangle in the 5 square unit is 1.

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