Advertisements
Advertisements
प्रश्न
In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)
पर्याय
1 : 2
2 : 1
1 : 3
3 : 1
उत्तर
1 : 3
Explanation;
Hint:
A line divides internally in the ratio m : n the point P
= `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`
(1, 6) = `((-2"m" + 2"n")/("m" + "n"), (3"m" + 7"n")/("m" + "n"))`
= `(-2"m" + 2"n")/("m" + "n")` = 1
−2m + 2n = m + nx
−3m = n – 2n
3m = n
`"m"/"n" = 1/3`
∴ m : n = 1 : 3
and
`(3"m" + 7"n")/("m" + "n")` = 6
3m + 7n = 6m + 6n
6m – 3n = 7n – 6n
3m = n
`"m"/"n" = 1/3`
APPEARS IN
संबंधित प्रश्न
Find the mid-point of the line segment joining the points:
(–6, 7) and (3, 5)
Given a line ABCD in which AB = BC = CD, B = (0, 3) and C = (1, 8). Find the co-ordinates of A and D.
One end of the diameter of a circle is (–2, 5). Find the co-ordinates of the other end of it, if the centre of the circle is (2, –1).
The co-ordinates of the centroid of a triangle PQR are (2, –5). If Q = (–6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.
Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).
Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.
ABC is a triangle whose vertices are A(-4, 2), B(O, 2) and C(-2, -4). D. E and Fare the midpoint of the sides BC, CA and AB respectively. Prove that the centroid of the Δ ABC coincides with the centroid of the Δ DEF.
A(3, 1), B(y, 4) and C(1, x) are vertices of a triangle ABC and G(3, 4) is its centroid. Find the values of x and y. Also, find the length of side BC.
Find the mid-point of the line segment joining the points
`(1/2, (-3)/7)` and `(3/2, (-11)/7)`
Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.
