Question

If L is the midpoint of AC, where A = -10 and C = 10, what are the coordinates of point L?

Answer 1

The coordinates of point L, the midpoint of AC where \(A = -10\) and \(C = 10\), are \((0, 0)\).

Step-by-step explanation:

To find the coordinates of the midpoint L between two given points A and C, we use the midpoint formula:

`\[ L_x = \frac{{A_x + C_x}}{2} \]`

`\[ L_y = \frac{{A_y + C_y}}{2} \]`

Given that \(A = (-10, A_y)\) and \(C = (10, C_y)\), substitute these values into the formula:

`\[ L_x = \frac{{-10 + 10}}{2} = 0 \]`

`\[ L_y = \frac{{A_y + C_y}}{2} \]`

Since the y-coordinate of A and C is not provided, we express the result in terms of \(A_y\) and \(C_y\). The final coordinates of point L are \((0, \frac{{A_y + C_y}}{2})\).

If the y-coordinates of A and C are known, the specific numerical values for \(A_y\) and \(C_y\) can be substituted to obtain the exact coordinates of point L. If the y-coordinates are not given, the expression
`\((0, \frac{{A_y + C_y}}{2})\)` represents the coordinates of L in terms of the unknown y-coordinates.