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=√((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=√((-1-3)^2+(3-(-4))^2)=√((-4)^2+(7)^2)=√(16+49)=√(65)`

Therefore, the distance between the given points A(3,-4) and B(-1,3) is:
`√(65)` or 8.06 (approx).