Question

AB and BC form a right angle at their point of intersection, B. If the coordinates of A and B are (14, -1) and (2, 1), respectively, the y-intercept of AB is ? and the equation of BC is y=? x +?. if the y-coordinate of point c is 13, its x coordinate is ? .

Answer 1

To find the y-intercept of line AB, we can use the point-slope form of a linear equation. The equation of line BC is y = -2x + 4, and the x-coordinate of point C is -4.5.

Step-by-step explanation:

To find the y-intercept of line AB, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Given the coordinates of point B (2, 1) and the fact that BC forms a right angle, we can calculate the slope of line AB as -2. Using the coordinates of either point A or B (let's use point B), we substitute the values into the point-slope form and solve for y:

1 - y1 = -2(x - x1)

1 - 1 = -2(x - 2)

0 = -2x + 4

y = -2x + 4

Therefore, the equation of line BC is y = -2x + 4. If the y-coordinate of point C is 13, we can substitute this value into the equation and solve for x:

13 = -2x + 4

9 = -2x

x = -4.5

Therefore, the x-coordinate of point C is -4.5.

Answer 2

Based on our conversation above, we can then easily find the missing x-coordinate. If the equation for line BC is y = 6*x - 11 and we know that the y-coordinate is 13, then

13 = 6*x - 11
24 = 6*x
4 = x

The x-coordinate is 4.