Find the distance from point A (-3; 4) to the midpoint of segment BC if: 1) B (3; 2), C (-1; 6) 2) B (-4; -3), C (2; 3 )

Let’s apply the formula for calculating the coordinates of the midpoint of the segment:

1) B (3; 2), C (-1; 6).

Find the midpoint of the segment using the formulas:

x = (x1 + x2) / 2 = (3 – 1) / 2 = 1;

y = (y1 + y2) / 2 = (2 + 6) / 2 = 4.

The midpoint of the segment has coordinates O (1; 4).

To calculate the length of a segment, apply the formula:

AO = √ ((x1 – x2) ^ 2 + (y1 – y2) ^ 2) = √ ((- 3 – 1) ^ 2 + (4 – 4) ^ 2) = √16 = 4.

The second option is similar.

2) B (- 4; – 3), C (2; 3).

We are looking for the coordinates of the middle of the segment:

x = (- 4 + 2) / 2 = -1;

y = (- 3 + 3) / 2 = 0.

The middle of the segment has coordinates:

O1 (-1; 0).

Cut length:

AO1 = √ ((- 3 + 1) ^ 2 + (4 – 0) ^ 2) = √ (4 + 16) = √20 = 2√5.