Given the coordinates of three points A, B, C. Make the equation of the straight line passing through the points A

| August 16, 2021 | education

Given the coordinates of three points A, B, C. Make the equation of the straight line passing through the points A and B and the equation of the perpendicular dropped from point C to line AB. A (2; 5) B (-3; 4) C (-4; -2)

Let us have the coordinates of three points A (2; 5), B (- 3; 4), C (- 4; – 2).
Let’s compose the equation of the straight line AB.
We know that AB: (x – x1) / (x2 – x1) = (y – y1) / (y2 – y1). Then we get that
AB: (x – 2) / (- 3 – 2) = (y – 5) / (4 – 5).
Then AB: y – 5 = (x – 2) / 5 or
y = x / 5 + 23/5.
The coefficient k1 of the straight AB is equal to: k1 = 1/5.
If the straight line is perpendicular to AB, then its coefficient should be k2 = – 1 / k1.
Hence k2 = – 5.
View of a straight line perpendicular to AB and passing through any point:
y = – 5x + b, where b is a constant. Since the straight line passes through point C, we have: – 2 = 20 + c. Hence в = – 22. Then the straight line has the form: у = – 5х – 22.
Answer: AB: y = x / 5 + 23/5, a straight line perpendicular to AB and passing through C:
y = – 5x – 22.



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