Question

A square ABCD is drawn in the first quadrant. If two of its vertices A and B lie on (2, 2)and (7, 2) respectively then write the coordinates of its other two vertices

Answer 1

Answer:

tO FIND: Coordinates of D & B ?

By distance formula:

Since DA = DC

=> (m+1)² + (n-2)² = (m-3)² + ( n-2)²

=> m² + 1 + 2m = m² + 9 - 6m

=> 6m + 2m = 9–1

=> m = 1 ……………(1)

Similarly,

P = 1 ………….(2)

Now, mid point O of diagonal DB, is calculated by section formula.. x =( x1 + x2)/2 & y=(y1+y2)/2

x =( 1+1)/2 = 1, y = (q + n)/2 …………..(3)

Now, the same mid point O of diagonal AC

x = (3- 1)/2 = 1, y = (2+2)/2 = 2 ……….(4)

By, …(3) & …..(4)

(q+n)/2 = 2

=> q+n = 4 ………………(5)

Now, since diagonals DB= AC , So, by distance formula

=> (n-q)² = 16

=> n-q = 4 …………..(6)

& n+q = 4 ………….(5)

=> 2n = 8

=> n = 4

=> q = 0

So, coordinates of D = ( 1, 4 )

& coordinates of B = ( 1, 0 )

Step-by-step explanation: