Question

Orthocentre of the triangle with vertices (4,1), (7,4), (5,-2) is​

Answer 1

Solution :-

given that, the vertices of the triangle are :-

• A = (4, 1)
• B = (7, 4)
• C = (5, -2)

Let us assume that,

• AD ⟂ BC .
• CF ⟂ AB .
• BE ⟂ AC .

so,

→ Slope of AB = (y2 - y1) / (x2 - x1) = (4 - 1) / (7 - 4) = 3/3 = 1

then,

→ Slope of CF = Perpendicular slope of AB

→ Slope of CF = (-1) / Slope of AB

→ Slope of CF = (-1) / 1

→ Slope of CF = (-1)

now, Equation of CF :-

→ y - y1 = m(x - x1)

→ y + 2 = (-1)(x - 5)

→ y + 2 = 5 - x

→ x + y = 3 ----------------- Eqn.(1)

Similarly,

→ Slope of BC = (y2 - y1) / (x2 - x1) = (-2 - 4) / (5 - 7) = (-6)/(-2) = 3

then,

→ Slope of AD = Perpendicular slope of BC

→ Slope of AD = (-1) / Slope of BC

→ Slope of AD = (-1) / 3

→ Slope of AD = (-1/3) .

now, Equation of AD :-

→ y - y1 = m(x - x1)

→ y - 4 = (-1/3)(x - 1)

→ 3y - 12 = -x + 1

→ x + 3y = 13 ----------------- Eqn.(2)

Subtracting Eqn.(1) from Eqn.(2) we get,

→ (x + 3y) - (x + y) = 13 - 3

→ x - x + 3y - y = 10

→ 2y = 10

→ y = 5

putting value of y in Eqn.(1) ,

→ x + 5 = 3

→ x = 3 - 5

→ x = (-2)

therefore, the orthocentre of the triangle are (-2 , 5) .

Learn more :-

find the centroid of the triangle whose vertices are (2, -3), (-4, 2)and(8, 13).

https://brainly.in/question/38194181

The orthocentre of the triangle with vertices A (1 , 3), B(2 , -1) and C ( 0 , -3)

https://brainly.in/question/35183021

Answer 2

Answer:

i want solution for that sum