Advertisements
Advertisements
प्रश्न
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.
पर्याय
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
उत्तर
Assertion (A) is true, but Reason (R) is false.
Explanation:
The coordinates of the point that divides a line segment with endpoints (x1, y1) and (x2, y2) in the ratio m:n are given by the section formula:
`((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`
Here, if the point (−3, k) divides the segment in the ratio 1: 2 between (−5, 4) and (−2, 3), then we can plug these values into the section formula:
`- 3 = (1(-2) + 2(-5))/(1 + 2)`
`- 3 = (- 2 - 10)/3`
`-3 = -4`
This is not true. Therefore, the x - x-coordinate does not satisfy the 1:2 division ratio.
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
S(0,5)
The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
The midpoint of the line segment joining A (2a, 4) and B (-2, 3b) is C (1, 2a+1). Find the values of a and b.
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
If the point `P (1/2,y)` lies on the line segment joining the points A(3, -5) and B(-7, 9) then find the ratio in which P divides AB. Also, find the value of y.
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
The abscissa and ordinate of the origin are
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The distance of the point (4, 7) from the x-axis is
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
The distance of the point (3, 5) from x-axis (in units) is ______.
