Question

# Two vertices of a triangle are (3,-2) and (-2,3) and its orthocentre is (-6,1). Then its third vertex is

- (1,6)
- (-1,6)
- (1,-6)
- None of these

Hint:

### The line passing through the orthocenter and the vertex is always perpendicular to it's opposite side.

## The correct answer is: (-1,6)

### Given That:

Two vertices of a triangle are (3,-2) and (-2,3) and its orthocenter is (-6,1). Then its third vertex is:

>>> Let the third vertex be (x, y) and I be the Orthocenter

>>> Then Slope of (3,-2) and (-2,3) becomes =

>>> Also, the slope of the IC is =

>>> We know the lines AB and IC are perpendicular. Then,

= 1

->> x+6=y-1

x-y+7=0

>>>Slope of AC is =

>>> Slope of IB =

>>> We know that the line IB is perpendicular to AC.

= -2

->> y+2 = -2x+6

2x+y-4=0

>>> By solving the above highlighted equations, we get the coordinates of third vertex as (-1,6).

>>> Therefore, the coordinates of the third vertex is (-1,6).

2x+y-4=0 and the x-y+7=0 are the equations that pass through the third vertex.

### Related Questions to study

### If in triangle , circumcenter and orthocenter then the co-ordinates of mid-point of side opposite to is :

>>> The orthocenter, centroid and circumcenter of any triangle are collinear. And the centroid divides the distance from orthocenter to circumcenter in the ratio $2:1$.

>>> Also, the centroid $(G)$ divides the medians $(AD)$ in the ratio $2:1.$

>>> ∴D(h, k)=(1,)

### If in triangle , circumcenter and orthocenter then the co-ordinates of mid-point of side opposite to is :

>>> The orthocenter, centroid and circumcenter of any triangle are collinear. And the centroid divides the distance from orthocenter to circumcenter in the ratio $2:1$.

>>> Also, the centroid $(G)$ divides the medians $(AD)$ in the ratio $2:1.$

>>> ∴D(h, k)=(1,)

### A triangle ABC with vertices A(-1,0), B(-2,3/4)&C(-3,-7/6) has its orthocentre H. Then the orthocentre of triangle BCH will be

### A triangle ABC with vertices A(-1,0), B(-2,3/4)&C(-3,-7/6) has its orthocentre H. Then the orthocentre of triangle BCH will be

### ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6 If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

$>>> acosθ=6$ ----(1)

$>>> a(sin(30−θ))=4$ ----(2)

>>> a =

### ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6 If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

$>>> acosθ=6$ ----(1)

$>>> a(sin(30−θ))=4$ ----(2)

>>> a =

### If the point lies between the region corresponding to the acute angle between the lines x-3y=0 and x-6y=0 then

>>> L11 L22 <0

>>> (1+cos)^{2} -6sin -6sincos -3sin-3sincos+18sin^{2} < 0

### If the point lies between the region corresponding to the acute angle between the lines x-3y=0 and x-6y=0 then

>>> L11 L22 <0

>>> (1+cos)^{2} -6sin -6sincos -3sin-3sincos+18sin^{2} < 0

### If be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is

((1+)+2() -1).() < 0

### If be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is

((1+)+2() -1).() < 0

### is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is

### is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is

### If the point ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

u ≡ x - 2y = 0 and v ≡ x - 4y = 0

>>> S(x, y) ≡ x² - 6xy + 8y² = 0

>>> ( a - 2 )( a - 4 ) < 0

### If the point ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

u ≡ x - 2y = 0 and v ≡ x - 4y = 0

>>> S(x, y) ≡ x² - 6xy + 8y² = 0

>>> ( a - 2 )( a - 4 ) < 0

### Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such is maximum is

Hence the point is (, ).

### Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such is maximum is

Hence the point is (, ).

### Assertion (A): The lines represented by and x+ y=2 do not form a triangle

Reason (R): The above three lines concur at (1,1)

Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

### Assertion (A): The lines represented by and x+ y=2 do not form a triangle

Reason (R): The above three lines concur at (1,1)

Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

### In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:

### In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:

### P_{1},P_{2},P_{3}, be the product of perpendiculars from (0,0) to respectively then:

P1 = 1;

P2 = ;

P3 = ;

>>> Therefore, we can say that P1>P2>P3.

### P_{1},P_{2},P_{3}, be the product of perpendiculars from (0,0) to respectively then:

P1 = 1;

P2 = ;

P3 = ;

>>> Therefore, we can say that P1>P2>P3.

### If θ is angle between pair of lines , then

>>> = 2.

>>> tan =

>>> = 10.

### If θ is angle between pair of lines , then

>>> = 2.

>>> tan =

>>> = 10.