Thread: Introduction to analytic geometry?

Can anyone assist me in these 2 questions

1. Find all values of a so that the distance between points (A,-9) and (-2A,7) is 20 units. I did this

Square root (7-(-9))^2+(-2a-a)^2

I get square root 256+9A=20 But how would I proceed taking the square root and the squaring 20?


My next question I am not sure how to start

Collinear points lie on the same line. Find the value of K for which the points (15,1)
(-3,8) and (3,k) are collinear.

Originally Posted by homeylova223

Can anyone assist me in these 2 questions

1. Find all values of a so that the distance between points (A,-9) and (-2A,7) is 20 units. I did this

Square root (7-(-9))^2+(-2a-a)^2

I get square root 256+9A=20 But how would I proceed taking the square root and the squaring 20?

Which variable are you solving for? A or a? Math is case sensitive!





Now square both sides and solve the quadratic.

Some advice...Write out the whole line each time, not just part of it. You'll see what you need to do more easily.

-Dan

Originally Posted by homeylova223

Collinear points lie on the same line. Find the value of K for which the points (15,1)
(-3,8) and (3,k) are collinear.

Recall the equation for a line: y = mx + b

Three points are colinear if they fall on the same line. So you have three equations:
1 = 15m + b
8 = -3m + b
k = 3m + b

Three equations, three unknowns. (Hint: solve the first two equations for m and b first.)

-Dan

Originally Posted by homeylova223

Collinear points lie on the same line. Find the value of K for which the points (15,1)
(-3,8) and (3,k) are collinear.

first find the slope m from the first 2 given points then use from this you should be able to see how to get

from this i got

now if you plug in 3 for x then y will give the k value