Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: points A, B, C, and D

Conjecture: A, B, C, and D are coplanar.

Question 16 options:

False; the four points do not have to be in a straight line.

True

False; two points are always coplanar but four are not.

False; three points are always coplanar but four are not.

False; three points are always coplanar but four are not.

Step-by-step explanation:

We are given points A, B, C and D. We say that a set of points are coplanar if there exists a plane that coints all the points. Consider A,B, C ,D points in a 3 dimensional space. It is true, by euclidean geometry, that given any 3 points in a 3 dimensional space, they are coplanar.

However, this is not true for 4 points.

Consider the points A=(1,0,0), B=(0,1,0), C=(0,-1,0) and D=(0,0,1). In this case, A,B and C are in the plane (x,y,0) and D is not coplanar to points A,B,C

i can't solve unless i know what the line is

step-by-step explanation:

welcome to/p>

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b