Question

PQRS is a square on a 1 cm square grid. If the coordinates of point P are (a, b) and those of point R are (c,d), what is the value of b-d?​

Answer 1

Explanation:

Since PQRS is a square, the distance between P and R along the y-axis must be equal to the distance between Q and S along the y-axis.

We know that the side length of the square PQRS is 1 cm, so the distance between P and R (or between Q and S) along the x-axis is also 1 cm.

Therefore, we have:

b - d = distance between P and R along the y-axis

= distance between Q and S along the y-axis

Looking at the grid, we can see that the y-coordinate of point Q is b+1, and the y-coordinate of point S is d+1.

So, the distance between Q and S along the y-axis is:

(b+1) - (d+1) = b - d

Therefore, b - d = 0.

So, the value of b-d is 0.