Question

Consider triangle ABC where A = (4,4), B = (7,4),
C = (4, 7) then find the orthocentre.​

Answer 1

Answer:

Of you plot these 3 points on x-y graph they will make a right angle triangle with right angle at point A. Hence coordinates of orthocentre are 4,4 Ans

Answer 2

Answer:

Orthocenter is vertex of A(4, 4)

Step-by-step explanation:

Given the points are A = (4, 4), B = (7, 4), C = (4, 7)

We have to find the Orthocenter

For a right angle triangle orthocenter is at the vertex.

that is where the right angle is placed .

First we prove that  ABC is a right angle triangle.

so we calculate the distances of AB, BC, CA.

Distance between two points (x1,y1) (x2,y2) is

d = √(x2 - x1)² + (y2 - y1)².

Distance of AB is

A = (4, 4), B = (7, 4)

AB  $=\sqrt{(7-4)^{2}+(4-4)^{2} } \\= \sqrt{9}\\=3$

B = (7, 4), C = (4, 7) distance is

$=\sqrt{(4-7)^{2}+(7-4)^{2} } \\=\sqrt{9+9} \\=\sqrt{18} \\=3\sqrt{2}$

A = (4, 4),  C = (4, 7) distance is

$= \sqrt{4-4^{2} +(7-4)^{2} } \\=\sqrt{9} \\=3$

Therefore, AB = 3, BC = 3√2, CA = 3

(BC)² = (AB)² +(CA)²

(3√2)² = (3)² +(3)²

18 = 9 + 9

Therefore, Triangle ABC is right angle.

Now we find the orthocenter

For a right angle triangle orthocenter is at the vertex.

that is vertex where the right angle is placed .

Orthocenter is vertex of A(4, 4)