Question

the coordinates of one endpoint of a line segment are 6,-2. The line segment is 4 units long . Which of the following is NOT a possible endpoint ?A.6,2B.6,-6C.10,-2D.-10,-2

Answer 1

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;

`D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

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;

`\begin{gathered} 4\text{ = }\sqrt[]{(6-6)^2+(-2-2)^2} \\ \\ 4\text{ = }\sqrt[]{0+(-4)^2} \\ \\ 4\text{ = }\sqrt[]{16} \\ \\ \end{gathered}`

Since the right hand side equals the left hand side, then this option is correct

Option B;

`\begin{gathered} 4\text{ = }\sqrt[]{(6-6)^2+(-2-(-6))^2} \\ \\ 4\text{ = }\sqrt[]{0+(4)^2} \\ \\ 4\text{ = }\sqrt[]{16} \end{gathered}`

since the left hand side equals the right hand side, then this option is correct

Option C;

`\begin{gathered} 4\text{ = }\sqrt[]{(10-6)^2+(-2-(-2))^2} \\ \\ 4\text{ = }\sqrt[]{4^2\text{ + 0}} \\ \\ 4\text{ = }\sqrt[]{16} \end{gathered}`

Since the left hand side is equal the right hand side, then this option is correct

Option D;

`\begin{gathered} 4\text{ = }\sqrt[]{(-10-6)^2+(-2-(-2))^2} \\ \\ 4\text{ = }\sqrt[]{(-16)^2\text{ + 0}} \\ \\ 4\text{ }\\e\text{ }\sqrt[]{256} \end{gathered}`

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