Advertisements
Advertisements
Questions
Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.
Determine the ratio in which the point P(m, 6) divides the line segment joining the points A (−4, 3) and B (2, 8). Also, find the value of m.
Advertisements
Solution
The co-ordinates of a point which divides two points (x1, y1) and (x2, y2) internally in the ratio m : n are given by the formula,
`(x, y) = ((mx_2 + nx_1) / (m + 2))"," ((my_2 + ny_1) / (m + n))`
Here, we are given that the point P(m, 6) divides the line joining the points A(−4, 3) and B(2, 8) in some ratio.
Let us substitute these values in the earlier-mentioned formula.
`(m, 6) = ((m(2) + n(-4)) / (m + n)), ((m(8) + n(3)) / (m + n))`
Equating the individual components, we have
`6 = ((m(8) + n(3)) / (m + n))`
6m + 6n = 8m + 3n
2m = 3n
`m / n = 3 / 2`
We see that the ratio in which the given point divides the line segment is 3 : 2.
Let us now use this ratio to find out the value of m.
`(m, 6) = ((m(2) + n(4)) / (m = n)), ((m(8) + n(3)) / (m + n))`
`(m, 6) = ((3(2) + 2(-4)) / (3 + 2)), ((3(8) + 2(3)) / (3 + 2))`
Equating the individual components, we have
`m = (3(2) + 2(4)) / (3 + 2)`
`m = -2 / 5`
Thus, the value of m is `- 2 / 5` and m : n = 3 : 2.
RELATED QUESTIONS
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
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.
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
Find the ratio in which the line segment joining the points A (3, 8) and B (–9, 3) is divided by the Y– axis.
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.
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
Write the X-coordinate and Y-coordinate of point P(–5, 4).
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
