Advertisements
Advertisements
प्रश्न
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Advertisements
उत्तर
The co-ordinates of the midpoint `(x_m, y_m)` between two points `(x_1, y_1)` and (x_2, y_2) is given by,
`(x_m,y_m) = (((x_1 + x_2)/2)"," ((y_1 + y_2)/2))`
Here we are supposed to find the points which divide the line joining A(-4,0) and B(0,6) into 4 equal parts.
We shall first find the midpoint M(x, y) of these two points since this point will divide the line into two equal parts
`(x_m, y_m) = (((-4+0)/2)","((0 + 6)/2))`
`(x_m, y_m) = (-2,3)`
So the point M(-2,3) splits this line into two equal parts.
Now, we need to find the midpoint of A(-4,0) and M(-2,3) separately and the midpoint of B(0,6) and M(-2,3). These two points along with M(-2,3) split the line joining the original two points into four equal parts.
Let M(e, d) be the midpoint of A(-4,0) and M(-2,3).
`(e,d) = (((-4-2)/2)","((0 + 3)/2))`
`(e,d) = (-3,3/2)`
Now let `M_2(g,h)` bet the midpoint of B(0,6) and M(-2,3).
`(g,h) = ((0 -2)/2)"," ((6 + 3)/2)`
`(g,h) = (-1, 9/2)`
Hence the co-ordinates of the points which divide the line joining the two given points are (-3,3/2), (-2, 3) and (-1, 9/2).
APPEARS IN
संबंधित प्रश्न
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
What is the distance between the points A (c, 0) and B (0, −c)?
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) ______.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
