Math Problem Statement

3. Diketahui M1 adalah pencerminan terhadap garis y=h dan M2 adalah pencerminan terhadap garis y=4, jika koordinat bayangan dari (M0, M1) (3, -1) adalah (3, -5) maka nilai h adalah... 4. Persamaan bayangan lingkaran x^2 + y^2 = 9 jika dicerminkan oleh garis y = -x dilanjutkan dengan pencerminan terhadap garis x=2 adalah... 5. Diketahui f(x) = (2x+3)/(2x-3) + x^2, direfleksi oleh y = x, dilanjutkan dengan dilatasi dengan skala 3 dan pusat (0,0). Hitung nilai g(3) !

Solution

I can see the questions from the image. Here's how I'll help break them down and solve each step-by-step:

3. Reflections and Coordinates

Question Summary: Two reflections, M1M_1 is a reflection over y=hy = h and M2M_2 is a reflection over y=4y = 4. The point (M,0,M1)=(3,1)(M, 0, M_1) = (3, -1) is reflected to (3,5)(3, -5). We are asked to find the value of hh.

Solution for Question 3:

  1. M1M_1 is the reflection of point (3,1)(3, -1) across y=hy = h.
  2. The result after two reflections (first across y=hy = h, then y=4y = 4) is (3,5)(3, -5).

Steps:

  • If a point is reflected across a line, the distance to that line remains equal, so after reflecting across y=hy = h, the intermediate reflection point will be symmetric with respect to hh.

Let me calculate that.

4. Circle Reflection over Lines

Question Summary: We have a circle x2+y2=9x^2 + y^2 = 9 reflected over y=xy = -x and then reflected again over x=2x = 2. We need to find the resulting equation.

Solution for Question 4:

  1. Reflecting over y=xy = -x: This transformation swaps xx and yy and negates both. Thus, reflecting x2+y2=9x^2 + y^2 = 9 over this line transforms the equation accordingly.
  2. Reflecting again over x=2x = 2: This reflection shifts the circle's center.

I will proceed with the transformations step-by-step.

5. Transformation of a Function

Question Summary: The function f(x)=2x+32x3+x2f(x) = \frac{2x+3}{2x-3} + x^2 is reflected over y=xy = x and then dilated by a scale factor of 3 from the center (0,0)(0,0). The task is to compute f(3)f(3).

Solution for Question 5:

First, we compute f(3)f(3), then apply the described transformations.

Let me first solve these questions individually. I'll start with calculations for question 3.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still walk you through the manual steps for solving each problem. Would you like me to continue explaining the solutions without calculations, or assist with another question?

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Math Problem Analysis

Mathematical Concepts

Geometric reflections
Transformations in geometry
Coordinate geometry
Circle equation
Algebraic functions

Formulas

Reflection across y = h
Reflection across y = -x
Reflection across x = 2
Function reflection: f(x) reflected over y=x
Dilation with scale factor

Theorems

Reflection theorem
Coordinate transformations
Dilation theorem

Suitable Grade Level

Grades 10-12