Option A: 25 units is the distance between the points
and
![(4,0)](https://img.qammunity.org/2021/formulas/mathematics/college/axhpluidkdqoumd0dd9hb5vz5sw2oq59g3.png)
Step-by-step explanation:
Given that the two coordinates
and
![(4,0)](https://img.qammunity.org/2021/formulas/mathematics/college/axhpluidkdqoumd0dd9hb5vz5sw2oq59g3.png)
We need to determine the distance between these two points.
The distance between the two points can be determined using the distance formula,
![d=√((x_2-x_1)^2+(y_2-y_1)^2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ykj4vnimechxgkuvrtfa2qltyc73jt9g88.png)
Substituting the coordinates in the formula, we get,
![d=√((4-0)^2+(0+3)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/xxnu1b1lsuxvxv4wjf6cxgszjk3jt1dzva.png)
Simplifying the terms within the bracket, we get,
![d=√((4)^2+(3)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/qwku14xa13sul55yfefqi33t9bqg7wzs1p.png)
Squaring the terms, we get,
![d=√(16+9)](https://img.qammunity.org/2021/formulas/mathematics/college/rmc7gu7msuczg0bmgmzpphboyhc1ehbql3.png)
Adding, we get,
![d=√(25)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5hd4qwntjv8mzwxlne5hk8g1tgx0uprdsk.png)
Simplifying, we have,
![d=5](https://img.qammunity.org/2021/formulas/mathematics/college/4rrto17gejft4rrcepjawz23szon8g87sf.png)
Thus, the distance between the two points is 5 units.
Therefore, Option A is the correct answer.