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Point [tex]\( M \)[/tex] is the midpoint of segment [tex]\( KL \)[/tex]. Point [tex]\( N \)[/tex] is the midpoint of segment [tex]\( ML \)[/tex].

Point [tex]\( K \)[/tex] is located at [tex]\((-7, -6)\)[/tex], and point [tex]\( L \)[/tex] is located at [tex]\((1, 10)\)[/tex]. What are the coordinates of point [tex]\( N \)[/tex]?

A. [tex]\((-5, -2)\)[/tex]

B. [tex]\((-1, 6)\)[/tex]

C. [tex]\((-3, 2)\)[/tex]


Sagot :

To find the coordinates of point [tex]\(N\)[/tex], we need to follow a series of steps carefully. Let's break it down step-by-step:

1. Determine the midpoint [tex]\(M\)[/tex] of segment [tex]\(KL\)[/tex]:

- Point [tex]\(K\)[/tex] has coordinates [tex]\((-7, -6)\)[/tex].
- Point [tex]\(L\)[/tex] has coordinates [tex]\((1, 10)\)[/tex].

The formula to find the midpoint [tex]\(M\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Plugging in the coordinates of points [tex]\(K\)[/tex] and [tex]\(L\)[/tex]:
[tex]\[ M_x = \frac{-7 + 1}{2} = \frac{-6}{2} = -3 \][/tex]
[tex]\[ M_y = \frac{-6 + 10}{2} = \frac{4}{2} = 2 \][/tex]

Therefore, the coordinates of point [tex]\(M\)[/tex] are [tex]\((-3, 2)\)[/tex].

2. Determine the midpoint [tex]\(N\)[/tex] of segment [tex]\(ML\)[/tex]:

- Point [tex]\(M\)[/tex] has coordinates [tex]\((-3, 2)\)[/tex].
- Point [tex]\(L\)[/tex] has coordinates [tex]\((1, 10)\)[/tex].

Again, using the midpoint formula:
[tex]\[ N = \left( \frac{M_x + L_x}{2}, \frac{M_y + L_y}{2} \right) \][/tex]

Plugging in the coordinates of points [tex]\(M\)[/tex] and [tex]\(L\)[/tex]:
[tex]\[ N_x = \frac{-3 + 1}{2} = \frac{-2}{2} = -1 \][/tex]
[tex]\[ N_y = \frac{2 + 10}{2} = \frac{12}{2} = 6 \][/tex]

Therefore, the coordinates of point [tex]\(N\)[/tex] are [tex]\((-1, 6)\)[/tex].

So, the coordinates of point [tex]\(N\)[/tex] are:
[tex]\[ \boxed{(-1, 6)} \][/tex]
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