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

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.

How to do?

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

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-

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.triangle is formed by joning three lines x+y-6=0,3y-x+2=0 and 3y=5x+2?find the orthocenter 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

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

Solution:Let BD be the bisector of $\angle $ABC. Then, AD : DC = AB : BCand AB = ${\sqrt{{\left(5+1\right)}^{2}+\left(1+7\right)}}^{2}=10$

BC = ${\sqrt{{\left(5-1\right)}^{2}+\left(1-4\right)}}^{2}=5$

∴ AD : DC = 2 : 1

By section formula, D $\equiv $( 1/3, 1/3)

Distance BD $\sqrt{{\left(5-\frac{1}{3}\right)}^{2}+{\left(1-\frac{1}{3}\right)}^{2}}=\frac{10\sqrt{2}}{3}$.

How did they come up with the first conclusion? AD:DC=AB:BC

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.

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 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

~~The sides of a triangle are given by the equation 3x+4y=10,4x-3y=5, and 7x+y+10=0. Show that the origin lies within the triangle.

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

(i) 2x+3y-4=0 and 2x+3y+17=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

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.

^{2}+ y^{2}+ 8x - 6y - 25 = 0 to the form AX^{2}+ BY^{2}= K^{2 }by shifting origin to a suitable point.^{}^{ 0}if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.

^{2 }-3(mx-ly)^{2 }and lx+my+n=0 form an equlateral triangle with area n^{2}/root3(l^{2}+m^{2})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.

^{1/2}= (x+2y-5)/n. Find n ?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.

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

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?

^{2},a) and (3,-2) lie on opposite sides of the line x+y+1=0 then belongs to the interval.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 bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

(i) ITS INTERCEPTS ON THE AXES (ANS IN THE TB : 3, -3/2)

(ii) THE LENGTH OF THE PORTION OF THE LINE INTERCEPTED BETWEEN THE AXES (ANS IN TB: 3√5/2)

(iii) THE SLOPE OF LINE ( ANS IN TB: 1/2)

How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?~~Put the equation 12y=5x+65 in the form of xcosθ+ysinθ=p and indicate clearly in a rough diagram the position of the straight line and the meaning of the constant θ and p.

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

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

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)

x

^{2}+xy-3y^{2}-y+2=0$ax+by+c=0;ax+by+c\text{'}=0;a\text{'}x+b\text{'}y+c=0a\text{'}x+b\text{'}y+c\text{'}=0$ are at right angles. Also find the equation to the diagonals of the parallelogram.

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

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?

Find the equation of the line which lies midway between the lines 2x+3y+7=0 and 2x+3y+5=0Find 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)

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

7. Equation of two equal sides of a triangle are the lines 7x + 3y - 20 = 0 and 3x + 7y - 20 = 0 and third side passes through the point (-3,3) then the equation of third side can be-

(A) x + y = 0

(B) x - y + 6 = 0

(C) x + 3 = 0

(D) y = 3

If

pandqare the lengths of perpendiculars from the origin to the linesxcosθ–ysinθ=kcos 2θandxsecθ+ycosecθ=k, respectively, prove thatp^{2}+ 4q^{2}=k^{2}Find the equation of the circle which passes through the points P(1,0), Q(3,0) and R(0,2). Find also

(i) The coordinates of the other point in which the axis of y cuts the circle,

(ii) The coordinates of the other end of diameter through Q.

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)Find the equation of a line on which perpendicular from the origin makes an angle of 30 degree with the x-axis and which forma a triangle of area 50/3^1/2 with the coordinate axes ?

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

~~A point P is such that the sum of the squares of its distances from the two axes of co-ordinates is equal to the square of its distance from the line x-y=1. Find the equation of the locus of P.

The slope of

x-axis is zero and the slope ofy-axis is not defined.HOW AND WHY ??A line passing through the point (3,0)makes an angle with 30degree with +ve direction of x-axis.

If this line is rotated through an angle of 15degree in clockwise direction , find its equation in new position.