Question

If A(-12,-8) and B(4,0) are given.find the co-ordinates of points P and Q which divide seg AB in the ratio 3/2:4/5 and 1.5:3.3 respectively. Then find co- ordinates of midpoint of seg PQ.​

Answer 1

Step-by-step explanation:

Given:-

A(-12,-8) and B(4,0) are given

To find:-

If A(-12,-8) and B(4,0) are given.find the co-ordinates of points P and Q which divide seg AB in the ratio 3/2:4/5 and 1.5:3.3 respectively. Then find co- ordinates of midpoint of seg PQ

Solution:-

Given points are A(-12,-8) and B(4,0)

Let (x1, y1) = (-12,-8)=>x1= -12 and y1 = -8

(x2, y2)=(4,0)=>x2 =4 and y2 =0

The ratio the point P which divides the linesegment AB = 3/2:4/5

=>m1:m2 = 3/2 : 4/5

=>m1 :m2 = (3/2)/(4/5)

=>(3/2)×(5/4)

=>15/8

m1:m2 = 15:8=>m1 = 15 and m2 = 8

The point P divides the points A(x1, y1) and

B(x2, y2) in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2) ,(m1y2+m2y1)/(m1+m2)]

=>P(x,y)

=[(15×4+8×-12)/(15+8) , (15×0+8×-8)/(15+8)]

=>[(60-96)/23,(0-64)/23]

=>P(x,y)=(-36/23,-64/23)

Given points are A(-12,-8) and B(4,0)

Let (x1, y1) = (-12,-8)=>x1= -12 and y1 = -8

(x2, y2)=(4,0)=>x2 =4 and y2 =0

The ratio the point Q which divides the linesegment AB = 1.5:3.3

=>m1:m2 = (15/10):(33/10)

=>m1 :m2 = (15/10)/(33/10)

=>(15/10)×(10/33)

=>15/33

m1:m2 = 15:33=>m1 = 15 and m2 = 33

The point P divides the points A(x1, y1) and

B(x2, y2) in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2) ,(m1y2+m2y1)/(m1+m2)]

=>Q(x,y)

=[15×4+33×-12)/(15+33),(15×0+33×-8)/(15+33)]

=>[(60-396)/48,(0-264)/48]

=>(-336/48,-264/48)

=>(-7,-11/2)

Q(x,y)=(-7,-11/2)

We have P(-36/23,-64/23) and Q(-7,-11/2)

Mid point of the linesegment PQ =

[ (x1+x2)/2,(y1+y2)/2]

=>[(-36/23-7)/2,(-64/23-11/2)/2]

=>[(-36-161)/46, (-128-253)/92]

=>(-197/46 ,-381/92)

Answer:-

The coordinates of P and Q are P(-36/23,-64/23) and Q(-7,-11/2) respectively.

The mid point of the line segment PQ is

(-197/46 ,-381/92)

Used formulae:-

• The point P divides the points A(x1, y1) and
• B(x2, y2) in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2) ,(m1y2+m2y1)/(m1+m2)]

• Mid point of the linesegment =
• [ (x1+x2)/2,(y1+y2)/2]

Answer 2

Answer:

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