Respuesta :
Option D; (-10,-2) is not a possible endpoint
Here, we want to select which of the options is not a possible end point of the line segment
Mathematically, the distance D between the end point of a line segment can be calculated using the formula;
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In the case of this question, D is 4.
So to get the odd option out, we will test the options one after the other till we have an answer.
Option A;
[tex]\begin{gathered} 4\text{ = }\sqrt[]{(6-6)^2+(-2-2)^2} \\ \\ 4\text{ = }\sqrt[]{0+(-4)^2} \\ \\ 4\text{ = }\sqrt[]{16} \\ \\ \end{gathered}[/tex]Since the right hand side equals the left hand side, then this option is correct
Option B;
[tex]\begin{gathered} 4\text{ = }\sqrt[]{(6-6)^2+(-2-(-6))^2} \\ \\ 4\text{ = }\sqrt[]{0+(4)^2} \\ \\ 4\text{ = }\sqrt[]{16} \end{gathered}[/tex]since the left hand side equals the right hand side, then this option is correct
Option C;
[tex]\begin{gathered} 4\text{ = }\sqrt[]{(10-6)^2+(-2-(-2))^2} \\ \\ 4\text{ = }\sqrt[]{4^2\text{ + 0}} \\ \\ 4\text{ = }\sqrt[]{16} \end{gathered}[/tex]Since the left hand side is equal the right hand side, then this option is correct
Option D;
[tex]\begin{gathered} 4\text{ = }\sqrt[]{(-10-6)^2+(-2-(-2))^2} \\ \\ 4\text{ = }\sqrt[]{(-16)^2\text{ + 0}} \\ \\ 4\text{ }\ne\text{ }\sqrt[]{256} \end{gathered}[/tex]Since what we have on the right hand side in this case is not equal to what we have on the left hand side, then this is the correct option
