In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the f
Practice Questions
Q1
In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?
AB is parallel to AC
AB is perpendicular to AC
AC is longer than AB
All sides are equal
Questions & Step-by-Step Solutions
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.
