In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the f

₹0.0

Question: In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?

Options:

Correct Answer: AB is perpendicular to AC

Solution:

The slope of AB is (6-2)/(4-1) = 4/3, and the slope of AC is (6-2)/(1-1) which is undefined. Since one slope is undefined, AB is perpendicular to AC.

In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?

In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?

Step 1: Identify the coordinates of the points A, B, and C. A is at (1, 2), B is at (4, 6), and C is at (1, 6).
Step 2: Calculate the slope of line segment AB using the formula (y2 - y1) / (x2 - x1). Here, y2 is 6 (from B) and y1 is 2 (from A), x2 is 4 (from B) and x1 is 1 (from A). So, the slope of AB is (6 - 2) / (4 - 1) = 4 / 3.
Step 3: Calculate the slope of line segment AC using the same formula. Here, y2 is 6 (from C) and y1 is 2 (from A), but x2 is 1 (from C) and x1 is 1 (from A). So, the slope of AC is (6 - 2) / (1 - 1). Since the denominator is 0, the slope is undefined.
Step 4: Determine if the lines are perpendicular. A line with an undefined slope is vertical, and a line with a defined slope (like AB) is not vertical. Therefore, AB is perpendicular to AC.

Slope of a Line – Understanding how to calculate the slope between two points and its implications for the relationship between lines.
Perpendicular Lines – Recognizing that if the slope of one line is undefined (vertical), it is perpendicular to a line with a defined slope.
Triangle Properties – Applying properties of triangles and understanding the significance of the points' coordinates.