Advertisements
Advertisements
प्रश्न
Find the coordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).
उत्तर
Let, M(x, y) be the midpoint of line PQ.
P(0, 6) = (x1, y1), Q (12, 20) = (x2, y2)
By the midpoint formula,
x = `(x_1 + x_2)/2`
= `(0 + 12)/2`
= `12/2`
= 6
y = `(y_1 + y_2)/2`
= `(6 + 20)/2`
= `26/2`
= 13
The coordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20) are M(6, 13).
APPEARS IN
संबंधित प्रश्न
Find the mid-point of the line segment joining the points:
(–6, 7) and (3, 5)
P(4, 2) and Q(–1, 5) are the vertices of parallelogram PQRS and (–3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.
A(–1, 0), B(1, 3) and D(3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.
The points (2, –1), (–1, 4) and (–2, 2) are mid-points of the sides of a triangle. Find its vertices.
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.
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–3, 7), Q(1, –4), a : b = 2 : 1
Find the midpoint of the line segment joining the following pair of point :
( -3, 5) and (9, -9)
Find the midpoint of the line segment joining the following pair of point :
(a+b, b-a) and (a-b, a+b)
Three consecutive vertices of a parallelogram ABCD are A(S, 5), B(-7, -5) and C(-5, 5). Find the coordinates of the fourth vertex D.
A( 4, 2), B(-2, -6) and C(l, 1) are the vertices of triangle ABC. Find its centroid and the length of the median through C.
The coordinates of the centroid I of triangle PQR are (2, 5). If Q = (-6, 5) and R = (7, 8). Calculate the coordinates of vertex P.
Two vertices of a triangle are ( -1, 4) and (5, 2). If the centroid is (0, 3), find the third vertex.
The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2 : 1 is
In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally
Find coordinates of midpoint of segment joining (– 2, 6) and (8, 2)
From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
