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answer with complete solution and plot it 

The equation of the line passing through point \( A(6, -2) \) and parallel to the line joining the midpoints of \( AB \) and \( AC \) is:

\[
y = 4x - 26
\]

This equation represents the line in slope-intercept form, with a slope of 4 and a y-intercept of -26. The plot above shows this line, along with the triangle's vertices \( A \), \( B \), and \( C \), and the midpoints of \( AB \) and \( AC \).

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Here are 5 related questions:
1. How do you find the midpoint of a line segment?
2. How would the equation change if the line passed through a different point?
3. How do you determine the slope between two points geometrically?
4. What would the equation of the line joining midpoints \( AB \) and \( AC \) be?
5. How can you verify that two lines are parallel?

**Tip:** The slope of a line remains the same for all parallel lines, only the intercept changes.

A triangle has its vertices at A(6, -2), B(2, 5), and C(0, -3). Find the equation of the line passing through A parallel to the line joining the midpoints of AB and AC.

In this problem, find the equation of the line passing through A(6, -2) parallel to the line joining the midpoints of AB and AC. Learn how to calculate midpoints and use the slope to determine the equation of a parallel line. Suitable for students in Grades 10-12.

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