This is a one-centimetre square grid - OCR - GCSE Maths - Question 5 - 2023 - Paper 3

To find the length of line AB, we can use the distance formula between two points A(-3, 3) and B(2, 3):

$ext{Distance} = ext{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$

Substituting the coordinates, we get:

$ext{Distance} = ext{sqrt}((2 - (-3))^2 + (3 - 3)^2) = ext{sqrt}((2 + 3)^2 + (0)^2) = ext{sqrt}(5^2) = 5$

Thus, the length of line AB is 5 cm.

To draw the line x = 2 on the grid, locate x = 2 on the x-axis. Then, draw a vertical line through this point that extends in both directions parallel to the y-axis, indicating all y-values at x = 2.

Since ABCD is a square and we already have points A and B, we need to use point B(2, 3) as a reference to find point C. Since point C should be at (2, y_c), where y_c will be the same distance as point D from A.

Given that the side length of the square is equal to the distance AB, which is 5 cm, we can find:

• Point C could be at (2, 3 + 5) = (2, 8) if we move upward.
• Point D should be directly across point C, having the same x-coordinate but differing y-coordinate. Thus, Point D coordinates can be (2, 3 - 5) = (2, -2).

Therefore, point D is at (2, -2).