From the uploaded image, the question involves mutually perpendicular lines drawn through a specific point $(2, 3)$ and intersecting another line $3x + 4y = 4$. The task is likely to find the equations of these lines or related properties.

Solution:

Step 1: Equation of a line through a point

The general equation of a line passing through $(2, 3)$ can be written as: $y - 3 = m(x - 2),$ where $m$ is the slope of the line.

Step 2: Condition for mutually perpendicular lines

If two lines are mutually perpendicular, the product of their slopes $m_1$ and $m_2$ satisfies: $m_1 \cdot m_2 = -1.$

Step 3: Intersection with $3x + 4y = 4$

The given line is $3x + 4y = 4$. Rewrite it in slope-intercept form: $y = -\frac{3}{4}x + 1.$ Thus, the slope of this line is $-\frac{3}{4}$.

Step 4: Finding intersection points

Let the two perpendicular lines passing through $(2, 3)$ have slopes $m_1$ and $m_2$ such that $m_1 \cdot m_2 = -1$. Substitute the equation of these lines into $3x + 4y = 4$ to find the points of intersection.

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