**Few problems based on transformation geometry are given below:**

**Problem 1:** A triangle whose vertices are (0, 4), (0, 0) and (6, 0) is enlarged to reach the vertices at (0 ,10), (0, 0) and (15, 0) respectively. Calculate the factor by which the triangle is enlarged.

**Solution:** Let the factor be k. For translation by factor "k", we have

(x, y) $\Rightarrow$ (k x, k y)

Here, (0, 4) $\Rightarrow$ (0, 10)

and (6, 0) $\Rightarrow$ (15, 0)

4 = 10 k

k = $\frac{10}{4}$ = 2.5

Also

15 = 6 k

k = $\frac{15}{6}$ = 2.5

Hence, the transformation factor is **2.5 unit**.

**Problem 2:** What would be the coordinates of point (7, -9), under the translation T$_{1, 2}$?

**Solution:** For translation, we have

T$_{a,b}$ : (x, y) $\Rightarrow$ (x + a, y + b)

Therefore,

T$_{1, 2}$ : (7, - 9) $\Rightarrow$ (7 + 1, -9 + 2)

So, (7, - 9) $\Rightarrow$ **(8, - 7)**.

**Problem 3:** Under reflection about X axis, what would be the coordinates of point (4, 5)?

**Solution:** For reflection, we know that

About X axis : (x, y) $\Rightarrow$ (x, - y)

Therefore,

(4, 5) $\Rightarrow$ **(4, - 5)**.