Question

Find the area of triangle formed by the line joining the points (1,7), (2,-5) with co ordinate axes

Answer 1

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Answer 2

Answer:

15 .041 square units is the required area .

Step-by-step explanation:

Explanation:

Given , the line joining the points  are (1 , 7) and  (2 , -5) .

Let   the points A (1 , 7 ) and B(2 , -5 )

Equation of line passing through point ($x_1, y_1$) and ($x_2 , y_2$) is

$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x- x_1)$

Step 1:

Two points are , A(1, 7 ) and B(2 , -5).

$x_1 = 1 , y_1 = 7 , x_2 = 2 and y_2 = -5$

So the equation of line passing through the point A(1,7) and (2 ,-5) is

$y - 7 = \frac{-5 - 7}{2 - 1 } (x- 1 )$

⇒y - 7 = -12 (x - 1)  ⇒ y - 7 = -12x + 12

⇒ 12x + y = 12 + 7 = 19

⇒12 x + y = 19

Divide both side by 19 we get ,

$\frac{12x}{19} + \frac{y}{19} = \frac{19}{19}$

⇒ $\frac{12x}{19} + \frac{y}{19} = 1$ , this satisfy the equation $\frac{x}{a} + \frac{y}{b} = 1$

Therefore , x intercept is a=  $\frac{19}{12}$   and  y intercept is  b = 19.

In ΔPOQ  , OQ  is base  = $\frac{19}{12}$ and OP is height  = 19 .

Area of triangle = $\frac{1}{2}$ × base × height .

⇒ Area = $\frac{1}{2}$ × $\frac{19}{12}$× 19

⇒ Area = $\frac{361}{24}$ =  15 .041 square units .

Final answer:

Hence , the area  of triangle  is  15 .041 square units .

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