Question

the perpendicular bisector of the line segment joining the points A(2,5) and B(3,8) cuts the y axis at

Answer 1

Step-by-step explanation:

Given: A(2,5) and B(3,8)

To find: The perpendicular bisector of the line segment joining the points A(2,5) and B(3,8) cuts the y axis at ?

Solution:

Tip: Perpendicular Bisector cuts the line at mid-point.

Equation of line passing through point (x1,y1) and have slope m is (y-y1)=m(x-x1)

Step 1: Find mid-point of AB,let it is C

$x = \frac{2 + 3}{2} \\ \\ x = 2.5 \\ \\ y = \frac{8 + 5}{2} \\ \\ y = 6.5$

C(2.5,6.5)

Step 2: Find slope of perpendicular bisector

Slope of line passing through points (x1,y1) and (x2,y2)

$m = \frac{y2 - y1}{x2 - x1}$

put the values

$m = \frac{8 - 5}{3 - 2} \\ \\ m = 3$

Slope of perpendicular bisector is = -1/3

Step 3: Find equation of perpendicular bisector

$y - 6.5 = \frac{ - 1}{3} (x - 2.5) \\ \\ y - 6.5 = - \frac{x}{3} + \frac{2.5}{3} \\ \\ y = - \frac{x}{3} + \frac{2.5}{3} + 6.5 \\ \\ y = - \frac{x}{3} + \frac{2.5 + 19.5}{3} \\ \\ y = - \frac{ x}{3} + \frac{22}{3}$

Step 4: Find y-intercept

Write slope intercept form and compare with equation of bisector and find y-intercept

y=mx+c

y intercept is 22/3

Final answer:

The perpendicular bisector of the line segment joining the points A(2,5) and B(3,8) cuts the y axis at 22/3.

Hope it helps you.

To learn more on brainly:

1) The perpendicular bisector of the line joining the points (2,5) and (3,6) cuts the y-axis at the point 1 a) (0, 5) b) (0...

https://brainly.in/question/46643307

2. The perpendicular bisector of the line

segment joining the points A(1,5) and B(4, 6)

cuts the y-axis at:

(a) (0, 13)...

https://brainly.in/question/39570674