Any 2 points determine a line. if there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?

Total number of lines formed by 6 points will be 15.

Step-by-step explanation:

Number of lines determined by 2 points = 1

There is a condition that only 2 points lie on a line.

Total number of points on a plane = 6

We have to calculate the number of lines formed by the pairs of these 6 points.

It's a question of combinations.

Number of combinations formed =

=

=

=

= 15

Therefore, total number of lines formed by 6 points will be 15.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.