Question

point A is on the y-axis at a distance of 4 units from the origin.If coordinates of point B are (-3,0) then find the length of AB.

Answer 1

Answer:

The length of AB will be 5 units

Step-by-step explanation:

Given that,

Point A is on y-axis at 4 unit

=> distance OA = 4

Point B lies at co-ordinate (-3,0)

=> distance OB = 3 units

since AOB is a right angled triangle, irrespective of the direction of point A with respect to the origin

hence according to Pythagoras theoram,

AB² = OA² + OB²

=> AB² = 4² + 3²

=> AB² = 16 + 9 = 25

=> AB = 5 units

Hence the length of AB will be 5 units

Answer 2

Answer:

Length of AB is 5

Step-by-step explanation:

Concept:

The distance between two points $(x_1,y_1)\:and\:(x_2,y_2)$ is

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

since the point A n y axis is at a distance of 4 units from origin ,

the coordinates of A is (0,4) or (0,-4)

when A(0,4) and B(-3,0)

$AB=\sqrt{(0+3)^2+(4-0)^2}\\\\AB=\sqrt{(3)^2+(4)^2}\\\\AB=\sqrt{9+16}\\\\AB=\sqrt{25}\\\\AB=5$

when A(0,-4) and B(-3,0)

$AB=\sqrt{(0+3)^2+(-4-0)^2}\\\\AB=\sqrt{(3)^2+(-4)^2}\\\\AB=\sqrt{9+16}\\\\AB=\sqrt{25}\\\\AB=5$