Advertisements
Advertisements
प्रश्न
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6). Find equations of the sides.
उत्तर
The vertices of triangle are A(1, 4), B(2, 3) and C(1, 6).
∴ equation of side AB is
`(y - 4)/(x - 1) = (3 - 4)/(2 - 1) = (-1)/1` = – 1
∴ y – 4 = –x + 1
∴ x + y = 5
Equation of side BC is
`(y - 3)/(x - 2) = (6 - 3)/(1 - 2) = 3/(-1)` = – 3
∴ y – 3 = – 3x + 6
∴ 3x + y = 9
Equation of side AC is
`(y - 4)/(x - 1) = (6 - 4)/(1 - 1) = 2/0`
∴ 0 = 2x – 2
∴ x = 1
Hence, equations of the sides of the triangle are x + y = 5, 3x + y = 9 and x = 1.
APPEARS IN
संबंधित प्रश्न
Obtain the equation of the line :
parallel to the Y−axis and making an intercept of 4 unit on the X−axis
Find the equation of the line passing through the points A(2, 0), and B(3, 4)
Find the equation of the line passing through the points P(2, 1) and Q(2, –1)
Find the equation of the line containing the origin and having inclination 60°
Find the equation of the line passing through the origin and parallel to AB, where A is (2, 4) and B is (1, 7)
Find the equation of the line having slope `1/2` and containing the point (3, −2).
Find the equation of the line containing point A(4, 3) and having inclination 120°
Find the equation of the line having inclination 135° and making X-intercept 7
Find the x and y intercept of the following line:
`x/3 + y/2` = 1
Find the x and y intercept of the following line:
2x − 3y + 12 = 0
Find equations of lines containing the point A(3, 4) and making equal intercepts on the co-ordinates axes.
Find the equations of perpendicular bisectors of sides of the triangle whose vertices are P(−1, 8), Q(4, −2), and R(−5, −3)
Select the correct option from the given alternatives:
If the point (1, 1) lies on the line passing through the points (a, 0) and (0, b), then `1/"a" + 1/"b"` =
Answer the following question:
Reduce the equation 6x + 3y + 8 = 0 into slope-intercept form. Hence find its slope
Answer the following question:
Obtain the equation of the line containing the point (2, 4) and perpendicular to the Y−axis
Answer the following question:
Find the equation of the line passing through the points S(2, 1) and T(2, 3)
Answer the following question:
Find the equation of the line which contains the point A(3, 5) and makes equal intercepts on the co-ordinates axes.
Answer the following question:
The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of altitudes of ∆ABC
Answer the following question:
Find the X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis
Answer the following question:
Two lines passing through M(2, 3) intersect each other at an angle of 45°. If slope of one line is 2, find the equation of the other line.
Answer the following question:
Find the equations of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11 and y = 12
Answer the following question:
A(1, 4), B(2, 3) and C(1, 6) are vertices of ∆ABC. Find the equation of the altitude through B and hence find the co-ordinates of the point where this altitude cuts the side AC of ∆ABC.
Answer the following question:
The vertices of ∆PQR are P(2, 1), Q(−2, 3) and R(4, 5). Find the equation of the median through R.
Answer the following question:
The perpendicular from the origin to a line meets it at (−2, 9). Find the equation of the line.
Answer the following question:
Show that there are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.
Answer the following question:
Show that there is only one line which passes through B(5, 5) and the sum of whose intercept is zero.
The lines `(x + 1)/(-10) = (y + 3)/-1 = (z - 4)/1` and `(x + 10)/(-1) = (y + 1)/-3 = (z - 1)/4` intersect at the point ______
The slope of normal to the curve x = `sqrt"t"` and y = `"t" - 1/sqrt"t"`at t = 4 is _____.
The point A(b, a) lies on the straight line 2x + 3y = 13 and the point B(a, b) lies on the straight line -x + 4y = 5, then the equation of line AB is ______
The intercept of a line between the coordinate axes is divided by the point (1, 3) in the ratio 3 : 1. The equation of the line will be ______
A Plane cuts the coordinate axes X, Y, Z at A, B, C respectively such that the centroid of the Δ ABC is (6, 6, 3). Then the equation of that plane is ______.
Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x – 12y = 0 be p and p', then ______.
Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to ______.
N(3, – 4) is the foot of the perpendicular drawn from the origin to a line L. Then, the equation of the line L is ______.
