Question

6. If the equations of the sides of a triangle
are 7x +y-10 = 0, x - 2y + 5 = 0 and
x +y+2 = 0, find the orthocenter of the
triangle​

Answer 1

Given:

The equations of the sides of a triangle  are 7x +y-10 = 0, x - 2y + 5 = 0 and  x +y+2 = 0

To find:

Find the orthocenter of the  triangle​

Solution:

From given, we have,

The equations of the sides of a triangle  are 7x + y - 10 = 0, x - 2y + 5 = 0 and  x + y + 2 = 0

Let the equation numbering be done as follows.

7x + y – 10 = 0 ⇒ (1),

x – 2y + 5 = 0 ⇒ (2),

x + y + 2 = 0 ⇒ (3)  

The point of intersection of the equations (2) and (3) is B (–3, 1).  

The equation of the altitude through B is given as,

(x + 3) – 7(y – 1) = 0  ⇒ x – 7y + 10 = 0 ⇒ (4)  

The point of intersection of the equations (3) and (1) is C(2, –4)  

The equation of the altitude through C is given as,

2(x – 2) + (y + 4) = 0  ⇒ 2x + y = 0  ⇒ (5)

Upon solving the equations (4) and (5), the orthocenter is obtained to be equal to (- 2/3, 4/3).

Therefore, the orthocenter of the  triangle​ is (-2/3, 4/3)

Answer 2

Step-by-step explanation:

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