Question

1) The co-ordinates of midpoint 1
of the segment joining the
points (15,19) and (3,1) are
O 18,10
0 9,10
O 18,20
O 28,20​

Answer 1

Answer:

1. Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:

(i) (2, – 3), ( – 6, 7)

(ii) (5, – 11), (4, 3)

(iii) (a + 3, 5b), (2a – 1, 3b + 4)

Solution:

Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

(i) Co-ordinates of midpoint of line joining the points (2, -3) and (-6,7) = {(2+-6)/2, (-3+7)/2}

= (-4/2, 4/2)

= (-2, 2)

Hence the co-ordinates of midpoint of line joining the points (2, -3) and (-6,7) is (-2, 2).

(ii) Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

Co-ordinates of midpoint of line joining the points (5, -11) and (4,3) = {(5+4)/2, (-11+3)/2}

= (9/2, -8/2)

= (9/2, -4)

Hence the co-ordinates of midpoint of line joining the points (5, -11) and (4,3) is (9/2, -4).

(iii) Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

Co-ordinates of midpoint of line joining the points (a+3, 5b) and (2a-1,3b+4) = {(a+3+2a-1)/2, (5b+3b+4)/2}

= {(3a+2)/2, (8b+4)/2}

= {(3a+2)/2, (4b+2)}

Hence the co-ordinates of midpoint of line joining the points (a+3, 5b) and (2a-1,3b+4) are {(3a+2)/2, (4b+2)}.

2. The co-ordinates of two points A and B are ( – 3, 3) and (12, – 7) respectively. P is a point on the line segment AB such that AP : PB = 2 : 3. Find the co-ordinates of P.

Solution:

Let the co-ordinates of P(x, y) divides AB in the ratio m:n.

A(-3,3) and B(12,-7) are the given points.

Given m:n = 2:3

x1 = -3 , y1 = 3 , x2 = 12 , y2 = -7 , m = 2 and n = 3

By Section formula x = (mx2+nx1)/(m+n)

x = (2×12+3×-3)/(2+3)

x = (24-9)/5

x = 15/5

x = 3

By Section formula y = (my2+ny1)/(m+n)

y = (2×-7+3×3)/5

y = (-14+9)/5

y = -5/5

y = -1

Hence the co-ordinate of point P are (3,-1).

plz make it as brilliant