Nathan drew a right triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3). AC is the longest side in ΔABC. What must be true for this triangle?

For making this statement true we have to check Triangle Inequality theorem.

Step-by-step explanation:

Given that,

Triangle ΔABC having three vertices are A (), B(), C () and AC is the longest side.

from the question,

Diagram of the given scenario is shown below,

According to Triangle Inequality theorem states that sum of any 2 sides of a triangle is always greater than third side.

Taking the ΔABC we have,

This condition must be satisfied for drawing a triangle if any two side sum is lesser than third side it will not form a triangle.

 Hence,

For making this statement true we have to check Triangle Inequality theorem.                                          

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answer: c

substitute in the values.

for a:

f(0) = 0 + 9

f(0) = 9

a is a solution.

for b:

f(7) = 14 + 9

f(7) = 23

b is a solution.

for c:

f (3) = 6 + 9

f(3) = 15

c is not a solution. it's supposed to be 14.

for d:

f(2) = 4 + 9

f(2)= 13

d is a solution.