**Educational Content: Understanding Transformations in Geometry****Problem Description**: You are given triangle LMN with the following vertices:- L(2, 7)- M(8, 8)- N(2, 1)Apply the transformation \( R_{y-axis} \circ T_{<-4,-5>} \) to the triangle and determine the new coordinates of point N', the image of point N after the transformation.**Transformation Explanation**:1. **Translation \( T_{<-4,-5>} \)**: - Move each point of the triangle left by 4 units and down by 5 units. - For point N(2, 1): - New x-coordinate: \( 2 - 4 = -2 \) - New y-coordinate: \( 1 - 5 = -4 \) - Resulting point after translation: N'(-2, -4)2. **Reflection Across the Y-axis \( R_{y-axis} \)**: - Reflect the point over the y-axis, meaning the x-coordinate changes sign while the y-coordinate remains the same. - For point N'(-2, -4) after translation: - Reflected x-coordinate: \( -(-2) = 2 \) - Y-coordinate remains: -4 - Resulting point after reflection: N'(2, -4)**Solution**:- The coordinates of N' after the transformations are (2, -4).**Important Concepts**:- **Translation** involves moving every point of a shape a certain distance in a specific direction.- **Reflection** is flipping a shape over a line, such as the y-axis, which changes the sign of the x-coordinate but keeps the y-coordinate the same.By understanding these transformations, you can accurately determine the new positions of geometric figures on the coordinate plane.

Given L(2,7)M(8,8)N(2,1) Translation Ry axis∘T(-4,-5) for rotation around y axis (x,y)→(-y,x)First rotate points around y axis Points after Ry axis L(2,7) L'(-7,2) M(8,8) M'(-8,8) N(2,1) N'(-1,2)now translation of T(-4,-5)(x,y)→(x-4,y-5) Points after Ry axis Ry axis∘T(-4,-5) L(2,7) L'(-7,2) L''(-11,-3) M(8,8) M'(-8,8) M''(-12,3) N(2,1) N'(-1,2) N''(-5,-3)