Question

the point P (a,b)is reflected in the x-axis to obtain point Q (3,-4) find a and b​

Answer 1

Basic Concept Used :-

How to find the co-ordinates of the reflection of a point in x-axis?

• To find the co-ordinates in the adjoining figure, x-axis represents the plain mirror. M is the point in the rectangular axes in the first quadrant whose co-ordinates are (h, k).

• When point M is reflected in x-axis, the image M’ is formed in the fourth quadrant whose co-ordinates are (h, -k). Thus we conclude that when a point is reflected in x-axis, then the x-co-ordinate remains same, but the y-co-ordinate becomes negative.

Thus,

• The image of point M (h, k) is M' (h, -k).

Rules to find the reflection of a point in the x-axis:

• (i) Retain the abscissa i.e., x-coordinate.

• (ii) Change the sign of ordinate i.e., y-coordinate.

Let's do the problem now!!

According to statement,

• Point P (a,b) is reflected in the x - axis.

• So the image of (a, b) in x - axis is (a, - b)----(1)

But,

It is given that

• Reflection of P (a,b) in x - axis is Q (3,- 4). -----(2)

From equation (1) and (2), we concluded that

$\rm :\longmapsto\:(a, - b) = (3,- 4)$

So, on comparing, we get

$\bf :\longmapsto\:a \: = \: 3 \: \: \: and \: \: \: b \: = \: 4$