Advertisements
Advertisements
प्रश्न
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
Advertisements
उत्तर
Since the point (x, y) lie on the line joining the points (1, −3) and (−4, 2); the area of triangle formed by these points is 0.
That is,
Δ `= 1/2 { x (- 3 -2 ) + 1 (2 - y ) - 4 (y + 3) } = 0`
- 5x + 2 - y - 4y - 12 = 0
- 5x - 5y - 10 = 0
x + y + 2 = 0
Thus, the result is proved.
APPEARS IN
संबंधित प्रश्न
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Find the ratio in which the line segment joining the points A (3, 8) and B (–9, 3) is divided by the Y– axis.
If (a,b) is the mid-point of the line segment joining the points A (10, - 6) , B (k,4) and a - 2b = 18 , find the value of k and the distance AB.
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
The points whose abscissa and ordinate have different signs will lie in ______.
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
