Find the coordinates of foot of perpendicular from the point (2,3) to the line 3x+4y+8=0.

• the coordinates of a point which is at a distance of 1/root2 units from (1,1) in the direction of line x + y - 3= 0
• answer is (1/2, 3/2)

Q.17 of miscellaneous  ex. of N cert book chapter 10 st. line

The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides

the equation of the perpendicular bisectors of sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0respectively. if the point is A (1,-2), find the equation of line BC.

Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.
If the equation of one of the diagonals is 11x + 7y = 4, find the equation
of the other diagonal.

A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5) obtain it's equation?

sir, can u explain me how to find tan inverse in log books..

find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.

also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle

Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)

 two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-

Find the equation of straight line whose intercepts on the axes are thrice as

The hypotenuse of a right angled triangle has its ends at points (1,3) and (-4,1).Find the equation of the legs (perpendicular sides) of the triangle.

Find the image of the point (1,2) in the line x-3y+4 =0

Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0

if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find

a) the equation of the median through A

b) the equation of altitude through B

c) the right bisector of BC

the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?

a) 7/ root 5

b) 7/ root 13

c) root 5

d) root 13

 NCERT - miscellaneous exercise  ch 10 Q-17

The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.

Show that the points A(7,10), B(-2,5) and C(3,-4) are the vertices of an isoceles right-angled triangle.

The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line

find the equation of the line through the intersection of the lines 2x+3y-4 = 0 and x-5y = 7 that has its intercept equal to -4.

the points A,Band C are(4,0),(2,2),and(0,6) respectively.AB produced cuts the y-axis at Pand CB produced cuts the x-axis at Q.find the co-ordinates of the pointsP and q.Find the eq. of the straight line joining the mid points of AC nad OB( Where O is the origin )and verify that this line passes through the mid point of PQ.

the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine

a) the equation of line AP

b) the co-ordinate of P

c) the area of triangle OAP, where O is origin

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

find the equation to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=0

find the distance of the point [3,2] from the straight line whose slope is 5 and is passing through the point of intersection of lines x+2y=5and x-3y+5=o

1. find the equation of perpendicular bisectors of the line segment joining the points (1,1) and (2,3)

2. Find the eq of the line which passes through the points (3,4) and the sum of its intercepts on the axes 14

Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0

One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its
vertices are (–3, 1) and (1,1). Find the equation of other three sides.

find the eqn of the line cutting off an intercept -2 from the y-axis and equally inclined to the axes.

if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.

Consider a family of straight lines (x + y) + lambda(2x - y + 1) = 0. Find the equation of the straight line belonging to this family that is farthest from (1, -3).

Kindly please don't refer me the link to a similar question that ha s already been answered as I tried that method but I got a wrong answer.

Thank You.

Find the eq. of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intetercepted between the axes of the coordinates.

the diagonal of a square lies along the line 8x-15y=0 one vertex is (1,2). find equations to the side of square passing through it?

Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

How to split a pair of line equation of ax²+2hxy+by²+2gx+2fy+c=0 in the short method?

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise. 

what difference it will get when  it become clockwise in place of  aticlockwise. 

find the equation of the line cutting off an intercept -2 from the y axis and equally inclined to the axis .

 find the equation of the straight line which cuts off intercepts on x axis twice that on y axis and is at a unit distance from the origin

find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line making an angle of 45degreewith the x axis

find what the following equation becomes when the origin is shifted to the point(1,1)

x²+xy-3y²-y+2=0

1. The base of an equilateral triangle lies along the line 9x+4oy-50=0 and its vertex lies on the line 9x+40y+32=0.Find the length of each side of the triangle and also find its area?
2. A traingle is formed by the the lines 3x+4y-60=0, 12x+5y-3=0 and 4x-3y+12=0.Find the internal bisector of the angle opposite to the sides 3x+4y-6=0?
3. The two sides of a square lie on the lines 5x-12y+26=0 and 5x-12y-65=0.Find its area?

if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?

what acute angle does a line of slope -2/3 make with vertical line.

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

find the equation of passing through the point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units away from the point (3,2)

find the locus of a point equidistant from the lines x+y+4=0 and 7x+y+20=0.

If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.

If p and q are the lengths of perpendiculars from the origin to the lines x cos θ – y sin θ = k cos 2θ and x sec θ+ y cosec θ = k, respectively, prove that p² + 4q² = k²

a straight line makes an intercept on the y axis twice as long as that on the x axis and is at a unit distance from the origin.determine its equation (pls slove it)

the lones x-2y+6=0 and 2x-y-10+0 intersect at P.Without finding the coordinates of prove that the equation of the line through P and the origin of coordinates is perpendicular to 39x+33y-580=0.

Find the equation of the line through the intersection of lines 3x + 4y = 7 and x – y + 2 = 0 and

find the equation of a straight line which passes through the point (4,-2) and whose intercept on y-axis is twice that on x-axis ?