Question

Darko found the distance between points A(3,-4) and B(-1,3) his work is shown below

Answer 1

We know that in two dimensional co-ordinate geometry, the distance,d, between any two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula:

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

We will use the above formula that Darko must have used to find the distance between the two points A(3,-4) and B(-1,3). In this case: $(x_1,y_1)=(3,-4)$ and $(x_2,y_2)=(-1,3)$.

Thus, the distance,$d=\sqrt{(-1-3)^2+(3-(-4))^2}=\sqrt{(-4)^2+(7)^2}=\sqrt{16+49}=\sqrt{65}$

Therefore, the distance between the given points A(3,-4) and B(-1,3) is: $\sqrt{65}$ or 8.06 (approx).