The three lines `4x -7y+ 10= 0,` `x+ y= 5` and `7x+ 4y= 15` form the sides of a triangle. Then the point (1, 2) is its (B) incentre (A) centroid (D) none of these (C) orthocentre

Explanation

`4x-7y+10 = 0->(1)`

`x+y = 5->(2)`

`7x+4y = 15->(3)`

Here, slope of line 1 `(m_1) = 4/7`

Slope of line 3, `(m_3) = -7/4`

`:. m_1**m_3 = 4/7**-7/4 = -1`

As, product of slope is `-1`, it means lines 1 and 3 are perpendicular to each other.

Now, we will find the intersection point of these two lines.

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