Question

two points A and B are in the first quadrant and O is the origin if the slope of OA is 1 the slope of OB is 7, and the length of OA is equal to the length of OB is equal to root 50 then the slope of AB is

Answer 1

for OA
slope = 1
angle = arctan 1 = 45 (no need to calculate, see the diagram)
x-coordinate of point A = √50 cos(45) = √50×(1/√2) = √25 = 5
y-coordinate of point A = √50 sin(45) = √50×(1/√2) = √25 = 5
Point A is (5,5)

for OB
slope = 7
angle = arctan 7 = 81.91  (no need to calculate, see the diagram)
x-coordinate of point A = √50 cos(81.91)= 1
y-coordinate of point A = √50 sin(81.91) = 7
Point B is (1,7)

Slope of line AB = (7-5)/(1-5) = 2/(-4) = -1/2

Answer 2

Answer:

Step-by-step explanation:

Let A be angle of OA with x-axis, and B be the angle of OB with x-axis.

Let m be the required slope. Let Q be the (in acute sense) angle made by AB with horizontal.

So m = -tanQ

 

Now tanA=1, or SinA=1/root2 and cosA=1/root2

and tanB=7, or SinB=7/root50 and cosB=1/root50.

 

From figure, tanQ = (sinB-sinA)/(cosA-cosB)

or tanQ = (7root2 - root50)/(root50 - root2) = (7-5)/(5-1) = 1/2

 

or required slope m = -1/2