Question

question 1
which statement is not an axiom of geometry?
any line segment can be extended indefinitely.
a straight line can be drawn between any two points.
all points exist on the same line.
all right angles are congruent.
question 2
which of the following is the midpoint between (-3, 8) and (4, -7)?
(0.5, 0.5)
(3.5, 0.5)
(3.5, 7.5)
(0.5, 7.5)

Explanation:

Question 1

In geometry, axioms are fundamental statements. "Any line - segment can be extended indefinitely", "A straight line can be drawn between any two points", and "All right angles are congruent" are well - known geometric axioms. However, not all points exist on the same line. There are non - collinear points in geometry.

Step1: Recall mid - point formula

The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1=-3,y_1 = 8,x_2 = 4,y_2=-7\).

Step2: Calculate the x - coordinate of the mid - point

\(x=\frac{-3 + 4}{2}=\frac{1}{2}=0.5\)

Step3: Calculate the y - coordinate of the mid - point

\(y=\frac{8+( - 7)}{2}=\frac{8 - 7}{2}=\frac{1}{2}=0.5\)

Answer:

C. All points exist on the same line.

Question 2