Question

Mid point $A(0,0)$ and $B(1024,2048)$ is $A_1$ and mid point of $A_1$ and $B$ is $A_2$ and so on. Coordinates of $A_{10}$ are:

• A. $(1022,2044)$
• B. $(1025,2050)$
• C. $(1023,2046)$
• D. $(1,2)$

Answer 1

The correct option is C $(1023,2046)$

REF. Image.

A is a mid point of $A(0,0)$ and $B(1024,2048)$

$A_1(\frac{1024+0}{2},\frac{2048+0}{2})=(512,1024)$

$A_2=(\frac{512+1024}{2},\frac{1024+2048}{2})=(\frac{1536}{2},\frac{3072}{2})=(768,1536)$

here, $A_2$

is a mid point of $A_1$ and B.

$\Rightarrow A_3$ is a midpoint of $A_2$ and B.

So,

$A_3=(\frac{768+1024}{2},\frac{1536+2048}{2})=(\frac{1792}{2},\frac{3584}{2})=(896,1792)$

$\Rightarrow A_4$ is midpoint of $A_3\&B-$

$A_4=(\frac{869+1024}{2},\frac{1792+2048}{2})=(960,1920)$

so, x coordinates of $A_1,A_2,A_3...$ are

So, x coordinate of $A_{10}$ is 1023.

Similarly for y-coordinates

So, y-coordinate of $A_{10}$ is 2046

$A_{10}(1023,2046)$

So, option (C) is right.