Answer:
The hikers are 5.9 miles apart.
Step-by-step explanation:
Let O represents the base camp,
Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,
Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.
By making the diagram of this situation,
Let D' is the point in the line AB,
Such that, AD' = CD
In triangle BD'D,
BD' = AB + AD' = 1.5 + 0.5 = 2 miles,
DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,
By Pythagoras theorem,


Hence, the hikers are 5.9 miles apart.
I think that first you need to understand what CPCTC is used for.
Let's start with the definition of congruent triangles.
Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.
A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.
Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.
Problem 1.
Statements Reasons
1. Seg. AD perp. seg. BC 1. Given
2. <ADB & <ADC are right angles 2. Def. of perp. lines
3. <ADB is congr. <ADC 3. All right angles are congruent
4. Seg. BD is congr. seg CD 4. Given
5. Seg. AD is congr. seg. AD 5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD 6. SAS
7. Seg. AB is congr. seg. AC 7. CPCTC
It is a bit tedious to write 6 equations, but it is a straightforward process to substitute the given point values into the form provided.
For segment ab. (x1, y1) = (1, 1); (x2, y2) = (3, 4).
... x = 1 + t(3-1)
... y = 1 + t(4-1)
ab = {x=1+2t, y=1+3t}
For segment bc. (x1, y1) = (3, 4); (x2, y2) = (1, 7).
... x = 3 + t(1-3)
... y = 4 + t(7-4)
bc = {x=3-2t, y=4+3t}
For segment ca. (x1, y1) = (1, 7); (x2, y2) = (1, 1).
... x = 1 + t(1-1)
... y = 7 + t(1-7)
ca = {x=1, y=7-6t}
Answer:

Step-by-step explanation:
Let points D, E and F have coordinates
and 
1. Midpoint M of segment DF has coordinates

2. Midpoint N of segment EF has coordinates

3. By the triangle midline theorem, midline MN is parallel to the side DE of the triangle DEF, then points M and N are endpoints of the midsegment for DEF that is parallel to DE.
Answer:
33 chips
Step-by-step explanation:
c= (700 - 464) ÷ 7 = 33
She can use 33 chips or less. I less cause she shouldn't eat too much calories.