Question

3. How many squares could be formed by connecting four of the 10 marked points of the
grid in the picture?
(C) 2
(A) 0
(D) 3
(B) 1
(E) 4​

Answer 1

Answer:

Let's take an example.

A square in which each side contains eight dots, has three possible vertical positions, and three possible horizontal positions:

Step-by-step explanation:

(10×10) dots ⟹1position(10×10) dots ⟹1position

(92) dots ⟹22 pos's(92) dots ⟹22 pos's

...

(10−n)2⟹(n+1)2(10−n)2⟹(n+1)2

...

22⟹9222⟹92

(12 dots 12 dots  is no square)

To sum {12+22+32+...+9212+22+32+...+92} we use the formula:

∑mn=1n2=16m(m+1)(2m+1)∑n=1mn2=16m(m+1)(2m+1)

Leading to a total of:

∑9n=1n2=169(9+1)(18+1)=285 squares

I think this may be helpful for you.

Plz,, Marks as brainlist.

Answer 2

Answer:

first answer is brainlist