Question

solve with steps explanation ✔​

Answer 1

Answer:

• B is (5, 11/2).   verify by finding AB and BC.

Step-by-step explanation:

Given points :   A = (3, 4) .    C(11, 10).  

Slope of straight line AC = (10 -4)/(11-3) = 3/4

Let the point B be (p, q).

Given the length of the line segment AB = 2.5.

A, B and C are collinear.

So  slope of AB = (q - 4)/(p - 3) = 3/4

So   4 q - 16 = 3 p - 9

       4 q = 3 p + 7    ----- (1)

AB² = (q - 4)² + (p - 3)² = 2.5² = 25/4

    p² + q² - 8 q - 6p + 75/4 = 0        --- (2)

(Length of segment AC)² = (10 - 4)² + (11 - 3)² = 100

Length AC = 10  

AB = 2.5...   So BC = 7.5

We need the point B (p, q) which divides the line joining A (3.4) and C( 11, 10) in the ratio =  1 : 3

So   p = (1*11+ 3*3)/(1+3) = 5  

     q = (1*10 + 3 * 4) /(1+3) = 11/2

SO B is (5, 11/2)

• We can verify the values by finding AB and BC.

Answer 2

Step-by-step explanation:

The present age of Tara is x years. Priya’s present is 4 years less than thrice of Tara’s present age.

What is the prThe present age of Tara is x years. Priya’s present is 4 years less than thrice of Tara’s present age.

What is the present age of Priya?esent age of Priya?