Question

the perpendicular bisector of the line segment joining the points A 1, 5 and b 4, 6 cut the y axis at which point ​

Answer 1

Answer:

(0,13)

Step-by-step explanation:

Perpendicular bisector = Cuts at mid point, and is perpendicular 

First find the mid point 

x coordinate = 1+4 / 2 = 2.5 

y coordinate = 5+6 / 2 = 5.5 

Mid point = (2.5, 5.5) 

Then find the slope of the bisector : 

Slope of the given line = (5-6) / (1-4) = 1/3 

Slope of given line multiplied by slope of bisector = -1 

Slope of bisector = -1 / (1/3) 

= -3 

Use the point slope form to find the bisector's formula : 

-3 = (5.5 - y) / (2.5 - x) 

-7.5 + 3x = 5.5 - y 

3x + y - 13 = 0 

Transform the formula into slope-intercept form 

3x + y - 13 = 0 

y = -3x + 13 

Because slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept 

Therefore the perpendicular bisector cuts the y-axis at (0,13) 

Answer 2

Answer:

Answer:

(0,13)

Step-by-step explanation:

Step-by-step explanation:

Perpendicular bisector = Cuts at mid point, and is perpendicular 

First find the mid point 

x coordinate = 1+4 / 2 = 2.5 

y coordinate = 5+6 / 2 = 5.5 

Mid point = (2.5, 5.5) 

Then find the slope of the bisector : 

Slope of the given line = (5-6) / (1-4) = 1/3 

Slope of given line multiplied by slope of bisector = -1 

Slope of bisector = -1 / (1/3) 

= -3 

Use the point slope form to find the bisector's formula : 

-3 = (5.5 - y) / (2.5 - x) 

-7.5 + 3x = 5.5 - y 

3x + y - 13 = 0 

Transform the formula into slope-intercept form 

3x + y - 13 = 0 

y = -3x + 13 

Because slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept 

Therefore the perpendicular bisector cuts the y-axis at (0,13)