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ML Aggarwal Solutions Class 10 Mathematics Solutions for Section Formula Exercise 11 in Chapter 11 - Section Formula

Question 51 Section Formula Exercise 11

A (2, 5), B ( – 1, 2) and C (5, 8) are the vertices of a triangle ABC. P and Q are points on AB and AC respectively such that AP : PB = AQ : QC = 1 : 2.

Show that PQ = 1/3 BC

Answer:

Solution:

The Euclidean distance formula is used to calculate the separation between two points on a two-dimensional plane.

M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Section Formula Question 51 Solution image

By distance formula, d(PQ) = √[(x2-x1)2+(y2-y1)2]

Points are P(1,4) and Q(3,6).

So x1= 1, y1 **= 4**

x2 **= 3, y2** **= 6**

d(PQ) = √[(x2-x1)2+(y2-y1)2]

d(PQ) = √[(3-1)2+(6-4)2]

d(PQ) = √[(2)2+(2)2]

d(PQ) = √(4+4)

d(PQ) = √8 = 2√2 ..(i)

By distance formula, d(BC) = √[(x2-x1)2+(y2-y1)2]

Points are B(-1,2) and C(5,8).

So x1= -1, y1 **= 2**

x2 **= 5, y2** **= 8**

d(BC) = √[(x2-x1)2+(y2-y1)2]

d(BC) = √[(5-(-1))2+(8-2)2]

d(BC) = √[(6)2+(6)2]

d(BC) = √(36+36)

d(BC) = √72 = √(36×2) = 6√2 ..(ii)

BC/3 = 6√2/3 = 2√2 = PQ

PQ = 1/3 BC.

Hence proved.

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