A is the point (0,6) and B is (4,0)
the line y=2x-3 cuts the y-axis at C. The perpendicular bisector of AB cuts the y-axis at D. Find the length of CD
Answers
Answer is 14/3 units.
Given:
A = (0,6) ; B = (4,0) and line y=2x-3 cuts Y- axis at C = (0,a) and perpendicular bisector of AB cuts Y- axis at D = (0,b)
Explanation:
As C = (0,a) is on Y- axis, it satisfies the given equation y=2x-3. So by substituting the point C in given equation, you get C = (0,-3).
Slope of equation AB= 0-6/4-0 = -3/2. By finding equation of AB, you get 3x+2y-12 = 0. As the product of slopes of Perpendicular lines is -1, you get slope of Perpendicular bisector of AB as 2/3.
NOTE: Perpendicular bisector of AB means the line passing through the mid point of AB and perpendicular to AB.
So, the equation of perpendicular bisector of AB passes through mid point of AB i.e, (2,3) and also is perpendicular to AB.
By finding equation of perpendicular bisector of AB, you get 2x-3y+5 = 0____(1)
The equation (1) passes through D = (0,b). By substituting D = (0,b) in equation (1), you get D = (0,5/3).
As you came to know the points C and D, now you can find the length using the formula √(x2-x1)² - (y2-y1)² and you get 14/3 units. Here (x1,y1) ; (x2,y2) are C and D points respectively.
IF YOU FIND THIS ANSWER HELPFUL, PLEASE MARK IT AS BRAINLIEST ANSWER.