The y intercept of line AB is and x-coordinate of point C is .
Further explanation:
Given information:
(a) AB and BC forms a right angle at their point of intersection B.
(b) The coordinate of point A is (14,-1) and point B is (2,1).
(c) The y-coordinate of the point C is 13.
Calculation:
The equation of line passing through point is as follows:
......(1)
Here, is the slope of the line.
The slope of the line passing through point and is calculated as below:
......(2)
Consider the point A(14,-1) as and B(2,1) as .
Now substitute 14 for , 2 for , -1 for and 1 for in equation (2) to obtain the slope of line AB.
Substitute 2 for , 1 for and for in equation (1) to obtain the equation of line AB.
To obtain the y-intercept substitute 0 for in above equation.
Since the line AB and BC are perpendicular to each other, the slope of line BC is obtained as follows:
Substitute for in above equation.
The line BC passes through point B therefore, the equation of line BC is obtained as follows:
Substitute 6 for , 2 for and 1 for in equation (1).
Since the y coordinate of point C is 13, to obtain the x-coordinate of point C substitute 13 for y in above equation.
Thus, the y intercept of line AB is and x-coordinate of point C is .
Learn more:
1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)
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2. Which is the graph of f(x) = (x – 1)(x + 4)?
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Answer details:
Grade: Middle school.
Subjects: Mathematics.
Chapter: Coordinate geometry.
Keywords: line, slope, equation, x-intercept, y-intercept, perpendicular, right angle, straight lines, x-value, y-value, point, intersection, y=mx+c, y-y1=m(x-x1), function, middle term split method, binomial, parabola, straight lines, quadratic, polynomial, function, expression, equation, coordinate geometry.