## Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Let (x1,y1) = (22,20)(x2,y2) = (0,16)Let co-ordinate of midpoint be A(x,y)By Midpoint formula x = (x1+x2)/2 and y = (y1+y2)/2x = (22+0)/2 = 11y = (20+16)/2 = 36/2 = 18Hence co-ordinates of midpoint are (11,18).

## 5. Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k .

Let P (x, y) , A (x1, y1) and B (x2, y2) and be the given points.Here, x = k, y = 7, x1 = 8, y1 = 9, x2 = 1, y2 = 2,By Section formula y = (my2+ny1)/(m+n)7 = m×2+n×9/(m+n)7 = 2m+9n/(m+n)7m+7n = 2m+9n7m-2n = 9n-7n5m = 2nm/n = 2/5Hence m:n = 2:5.By Section formula, x = […]

## Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, -3) and (-2, 0) respectively.

Given co-ordinates of P = (-2,0) = (x,y)Co-ordinates of A = (2,-3) = (x1, y1)Let co-ordinates of B = (x2,y2)Since P is the midpoint of diameter AB ,By midpoint formula x = (x1+x2)/2-2 = 2+x2/2×2 = -4-2×2 = -6y = (y1+y2)/20 = (-3+y2)/2-3+y2 = 0y2 = 3Hence the co-ordinates of point B is (-6,3).

## Find the ratio in which point T(-1, 6)divides the line segment joining the points P(-3, 10) and Q(6, -8).

Let, point T(-1,6) divides segment PQ in the ratio m:nGiven P(-3, 10) and Q(6, -8).x = -1 , y = 6×1 = -3 , y1 = 10×2 = 6 , y2 = -8By Section formula, x = (mx2+nx1)/(m+n)-1 = m×6+n×-3/(m+n)-1 = 6m-3n/(m+n)-m+-n = 6m-3n2n = 7mm/n = 2/7m:n = 2:7Point T divides PQ is the ratio 2:7.

## In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.

(1) Let the co-ordinates of A be (x, y).P(-3, 7) and Q(1, -4) are the given points.x1 = -3 , y1 = 7 , x2 = 1 , y2 = -4 , m = 2 and n = 1By Section formula x = (mx2+nx1)/(m+n)x = (2×1+1×-3)/(2+1)x = -1/3By Section formula y = (my2+ny1)/(m+n)y = (2×-4+1×7)/3y = (-8+7)/3y = -1/3Hence […]

## Find the coordinates of point P if P divides the line segment joining the points A(-1,7) and B(4,-3) in the ratio 2:3.

Let the co-ordinates of P be (x, y).A(-1,7) and B(4,-3) are the given points.x1 = -1 , y1 = 7 , x2 = 4 , y2 = -3 , m = 2 and n = 3By Section formula x = (mx2+nx1)/(m+n)x = (2×4+3×-1)/(2+3)x = (8-3)/5x = 5/5x= 1By Section formula y = (my2+ny1)/(m+n)y = (2×-3+3×7)/5y = (-6+21)/5y = 15/5y […]