Which point is farthest from point K?

Looking at the line segment in the image, we can see the points labeled A, B, C, D, E, and M. Point K is located above point A. We need to determine which of the points A, D, B, E, or K is farthest from K.

To do this, we can visually compare the distances.

• Point A is directly below K, so the distance between K and A is the vertical distance between them.
• Points B, C, D, E, and M are located along the horizontal line.
• The distance from K to any point on the horizontal line will be the hypotenuse of a right triangle, where one leg is the vertical distance (from K to the line) and the other leg is the horizontal distance from A to that point.
• Visually, point M appears to be the farthest point along the horizontal line from point A. Therefore, the distance from K to M will be the largest.

Comparing the options given:

• The distance from K to A is the vertical distance.
• The distance from K to D involves a horizontal distance from A to D plus the vertical distance.
• The distance from K to B involves a horizontal distance from A to B plus the vertical distance.
• The distance from K to E involves a horizontal distance from A to E plus the vertical distance.
• The distance from K to M involves a horizontal distance from A to M plus the vertical distance.

Since M is the farthest point to the right of A, the distance from K to M will be the greatest.

However, the options provided are K, D, A, E, B. We need to select the farthest from these options.

• Distance K to A: Vertical distance.
• Distance K to D: Hypotenuse of triangle with legs: (vertical distance K to line) and (horizontal distance A to D).
• Distance K to B: Hypotenuse of triangle with legs: (vertical distance K to line) and (horizontal distance A to B).
• Distance K to E: Hypotenuse of triangle with legs: (vertical distance K to line) and (horizontal distance A to E).

We can observe that the horizontal distances increase as we move from A towards M. So, A is closest horizontally to A, B is next, then D, then E, and finally M is farthest.

Therefore, among the given options (A, B, D, E), the point E is the farthest from A horizontally, and thus will be farthest from K.

Ответ: E