Question 15 (i) Write down the co-ordinates of the point A and the point B on the diagram - Junior Cycle Mathematics - Question 15 - 2014

The distance formula is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For points A(0, 3) and B(4, 0), we calculate:

$|AB| = \sqrt{(4 - 0)^2 + (0 - 3)^2}$ $= \sqrt{16 + 9}$ $= \sqrt{25}$ $= 5$

The distance from the origin O(0,0) to A(0,3) is:

$|OA| = 3$

The distance from the origin O(0,0) to B(4,0) is:

$|OB| = 4$

Using the Pythagorean theorem:

$|AB|^2 = |OA|^2 + |OB|^2$ $|AB|^2 = 3^2 + 4^2$ $|AB|^2 = 9 + 16$ $|AB|^2 = 25$

Taking the square root:

$|AB| = \sqrt{25} = 5$