The ordinate of a point 𝐴 on 𝑦 − 𝑎𝑥𝑖𝑠 is 5 and 𝐵 has coordinates (− 3, 1). Find the length of 𝐴𝐵.

We are given the ordinate of point 𝐴 and the coordinates of point 𝐵.

The ordinate of a point means that the point lies on the 𝑦 − 𝑎𝑥𝑖𝑠 and its 𝑥 − coordinate is zero.

So, coordinates of point 𝐴, (𝑥, 𝑦) = (0, 5)

And the coordinates of point 𝐵, (𝑥', 𝑦') = (− 3, 1)

The distance between two points whose coordinates are given is equal to the length of the line formed by joining the points

So, length of 𝐴𝐵 = $\sqrt{{(x\text{'}-x)}^2} + {\left(y\text{'}-y\right)}^2$

Putting the values in the above equation, we get 

Length of 𝐴𝐵 = $\sqrt{{(3-0)}^2} + {\left(1-5\right)}^2$

Length of 𝐴𝐵 = $\sqrt{25}$ = 5 units

Hence, the length of 𝐴𝐵 is 5 𝑢𝑛𝑖𝑡𝑠.