Reflection in Quants? Isn’t this a physics concept we learned back in school?

- Well, yes, it is. However, a similar topic, which works on the same principle, is present in mathematics too.

Reflection in mathematics or quant takes place in the cartesian or coordinate plane and not in real-life space. Let us discuss this in detail.

**Reflection of a Point**

Most of the questions that come in GMAT are for a point or a line.

In this article, we are going to cover some advanced concepts of coordinate geometry, starting with the reflection of a point.

- the x-axis,
- the y-axis,
- the origin,
- the lines x = y,
- and x = – y

**Reflection on the x-axis **

- Let us take a
**point A (2, 3)**
- Now, if we reflect this point about the x-axis then it means the point will go to the other side of the x-axis (shown in the diagram)

- Remember that the reflected point (A’ in this case) and the original point (A in this case) are always equidistant from the line about which the reflection is taken (x-axis in this case).

- Let us take
** another point** **say (-3, 2)**, now, if we reflect this point on the x-axis, then notice that once again *the sign of the y coordinate will change* and the coordinate of the reflected point will be (-3, -2).

*Thus, if the point (x, y) is reflected about the x-axis, then the co-ordinate of the reflected point is (x, -y)*

**Reflection on the y-axis **

If want to reflect the **same point (2,3)** about the y-axis, then the reflected point will be (-2,3)

See, in this case, *the value of the y-co-ordinate does not change*.

- It is the sign of the x coordinate that is changing because it is moving from the positive side of the x-axis to the negative side.

Let us take **another point (3, -2)**. If we reflect this point about the y-axis, we’ll get the reflected point as (-3, -2).

*Hence, in this case, we can say if the point (x, y) is being reflected about the y-axis, then the co-ordinate of the reflected point will be (-x, y)*

**Reflection on the origin **

If we want to reflect the **same point (2, 3)** about the origin, then that point will be (-2, -3)

- In this case the
**sign of both x and y coordinate changes **

**Another example** can be the point (1, -2) which if we reflect on the origin, we get (-1, 2).

**Hence, in this case, we can say if the point (x, y) is being reflected about the origin, then the co-ordinate of the reflected point will be (-x, -y) **

**Reflection on the line X = Y **

This is another case, that we can encounter while solving coordinate geometry question

- We know that the x = y line passes through the origin and makes an acute angle (45° precisely) with the positive side of the x-axis.

- Now if we take a point, say (2, 3), and reflect it about the line x = y, then the
**coordinate of the reflected point will just get reversed** and it becomes (3, 2).

**So, if we have point (x, y) and we reflect it about the line x = y, then in that case, we get the reflected point as (y, x) **

**Reflection about the line X = – Y **

We know that the x = -y line also passes through the origin but the only difference is that it has a negative slope.

- This means that it makes an obtuse angle (135° precisely) with the positive side of the x-axis

- If we take the point (2, 3) and reflect it about the line x = -y, then the coordinates that we’ll get will be
**reversed in value and signs.** Here the reflected point will be (-3, -2)

**All we need to remember is that if we have point (x, y) and we reflect it about the line y = -x, then in that case, we get the reflected point as (-y, -x)**

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Reflection in Quants? Isn’t this a physics concept we learned back in school?

Reflection in mathematics or quant takes place in the cartesian or coordinate plane and not in real-life space. Let us discuss this in detail.

Reflection of a PointMost of the questions that come in GMAT are for a point or a line.

In this article, we are going to cover some advanced concepts of coordinate geometry, starting with the reflection of a point.

Reflection on the x-axispoint A (2, 3)another pointsay (-3, 2), now, if we reflect this point on the x-axis, then notice that once againand the coordinate of the reflected point will be (-3, -2).the sign of the y coordinate will changeThus, if the point (x, y) is reflected about the x-axis, then the co-ordinate of the reflected point is (x, -y)Reflection on the y-axisIf want to reflect the

same point (2,3)about the y-axis, then the reflected point will be (-2,3)See, in this case,

.the value of the y-co-ordinate does not changeLet us take

another point (3, -2). If we reflect this point about the y-axis, we’ll get the reflected point as (-3, -2).Hence, in this case, we can say if the point (x, y) is being reflected about the y-axis, then the co-ordinate of the reflected point will be (-x, y)Reflection on the originIf we want to reflect the

same point (2, 3)about the origin, then that point will be (-2, -3)sign of both x and y coordinate changesAnother examplecan be the point (1, -2) which if we reflect on the origin, we get (-1, 2).Hence, in this case, we can say if the point (x, y) is being reflected about the origin, then the co-ordinate of the reflected point will be (-x, -y)Reflection on the line X = YThis is another case, that we can encounter while solving coordinate geometry question

coordinate of the reflected point will just get reversedand it becomes (3, 2).So, if we have point (x, y) and we reflect it about the line x = y, then in that case, we get the reflected point as (y, x)Reflection about the line X = – YWe know that the x = -y line also passes through the origin but the only difference is that it has a negative slope.

reversed in value and signs.Here the reflected point will be (-3, -2)All we need to remember is that if we have point (x, y) and we reflect it about the line y = -x, then in that case, we get the reflected point as (-y, -x)## Related posts:

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