Question

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) (b) (0, 13) (c) (0, 12) (d) (13, 0)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given: A(1,5) and B(4,6)

To find: 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)

(b) (0, -13)

(C) (0, 12)

(d) (13,0)

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

$x = \frac{1 + 4}{2} \\ \\ x = 2.5 \\ \\ y = \frac{6 + 5}{2} \\ \\ y = 5.5$

C(2.5,5.5)

Step 2: Find slope of perpendicular bisector

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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

put the values

$m = \frac{6 - 5}{4-1} \\ \\ m = \frac{1}{3}$

Slope of perpendicular bisector is = -3

Step 3: Find equation of perpendicular bisector

$y - 5.5 = -3(x - 2.5) \\ \\ y - 5.5 = - 3x + 7.5 \\ \\ y = -3x+ 7.5+ 5.5 \\ \\ y = - 3x + 13$

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 13, Coordinates are (0,13)

Final answer:

The perpendicular bisector of the line segment joining the points A(1,5) and B(4,6) cuts the y axis at (0,13).

Option A is correct.

Hope it helps you.

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