# On the coordinate line, points A and A1 are symmetric about point P (1) If: 1) A (3),

**On the coordinate line, points A and A1 are symmetric about point P (1) If: 1) A (3), 2. A (-2), 3. A (-4), 4. A (5) Find the coordinate of point A1.**

If points A and A1 are symmetrical about point P, then the distance between points A and P is equal to the distance between points A1 and P. That is, the length of the segment AP is equal to the length of the segment A1P.

If you need to find the coordinate of the center of symmetry, for example, for points O (-9) and K (5):

It is necessary to find the length of the segment between the symmetric points, the length of the segment is equal to the modulus of the difference in the coordinates of the points, that is, | -9 – 5 | = | -14 | = 14;

divide the length of the segment in half, 14: 2 = 7;

set aside from the point located to the left (from the point O (-9)), to the right 7 unit segments, (-9) + 7 = (-2);

or set aside from the point located to the right (from the point K (5)), to the left 7 unit segments, 5 – 7 = -2;

the coordinate of the center of symmetry has coordinate (-2).

Algorithm for finding a symmetric point

If the coordinates of one of the symmetric points and the center of symmetry are known, then you need to find the length of the segment between the point and the center of symmetry and postpone the same segment to the other side of the center of symmetry.

For example: given point B (8) and center of symmetry O (2). Let’s find the length of the segment IN: | 8 – 2 | = | 6 | = 6. Point B is located to the right of point O, which means that we put off to the left of point O 6 unit segments: 2 – 6 = -4. The coordinate of the point symmetrical to point B is (-4).

Find the coordinate of point A1

By condition: coordinate of the center of symmetry P (1).

1) A (3).

Let’s find the length of the segment PA: | 3 – 1 | = 2. Point A lies to the right of point P, therefore, to the left of point P, we postpone 2 unit segments: 1 – 2 = -1.

The coordinate of point A1 is (-1).

2) A (-2).

We find the length of PA: | -2 – 1 | = | -3 | = 3. Point A lies to the left of point P, so we move to the right of point P by 3 unit segments: 1 + 3 = 4.

The coordinate of point A1 is (4).

3) A (-4).

Let’s find the length of the segment PA: | -4 – 1 | = | -5 | = 5. Point A lies to the left of point P, so we move to the right of point P by 5 unit segments: 1 + 5 = 6.

The coordinate of point A1 is (6).

4) A (5).

Let’s find the length of the segment PA: | 5 – 1 | = 4. Point A lies to the right of point P, therefore, to the left of point P, we postpone 4 unit segments: 1 – 4 = -3.

The coordinate of point A1 is (-3).