Can you help me with my math homework?

Question

I have this math packet to do and I have had problems with a few of them. Could you help me out, please?

1. What is the expression of the line that passes through (2,5) and is parallel to the x axis?

2. The length of line segment joining the two midpoints of two sides of equilateral triangle ABC is 5. Find the perimeter of ABC.

3. In triangle ABC, MN is parallel to AB, AC= 8, AB= 12 and CM=6. Find the length of MN.

Even just telling me how to these problems would be greatly appreciated!

Answer 1

Parallel to the x-axis means the y value never changes. They have given us a point which has a y value of 5. Therefore, the entire line has a y value of 5.
Answer:
y = 5

If you draw this out on paper, you'll see that the problem has divided the larger triangle into a trapezoid and a small triangle on top, still equilateral. This means that all of the side lengths of this small triangle are 5. Since the two side lengths that are part of the larger triangle run from the midpoint of the larger side to the end of it, those smaller side lengths, 5, are equal to half the side length of the larger side. Therefore, the side length of the large triangle is 10, multiplied by three sides.
Answer:
30

This problem is almost unsolvable without the picture that must have come with it. As I understand it, they imply that line segment MN is contained entirely within the triangle, and segments the triangle into a smaller triangle and a trapezoid, neither of them regular. The width of a triangle decreases linearly, starting at a side length and ending with its opposite angle. If we place point M on AC, then the distance between M and A is 2. This means that MN is 1/4 of the way up the triangle. Therefore, if point M is on AC, then MN will have 1/4 of the length of AB.

However, if point M is on BC, and ABC is scalene, then the problem is unsolvable. We have no way of knowing the length of BC, if triangle ABC is scalene. If it is isosceles, then BC is either 8 or 12. If BC is 8, then our answer is still 9, since AC and BC are identical. If BC is 12, then MN is half of AB, since MN would be situated halfway up the triangle.

Answer: 9, 6, or unknown

Answer 2

(1) slope = 0 (it's a horizontal line)

goes through (2,5)

use slope intercept form

y = Mx + b where M = slope = 0

if it goes thought (2,5) then y = 0x + b must mean y = 5

(2) If you draw an equilateral triangle

find the midpoints of the sides

draw a line connecting them, and make that 5 units long

you have drawn a smaller equilateral triangle sides 5,5 and 5 units (can you prove this?)

This means that half the length of the side of the big triangle is 5

the full length of the big triangle is 10

the big triangle has 3 sides making the perimeter ...

(3) Can you tell us where the line MN is drawn? Is it outside the triangle, cutting through the triangle or what?

I'll assume MN cuts through the triangle

M is a point on AC
N is a point on BC
MN is parallel to AB

CM is 6

MN/AB = 6/8 because the triangles ABC and MNC are similar triangles

So MN = 9

OMG just LOOK at these answers below. You'll have to do the maths yourself and not trust the arithmetic of the general internet population.

*boggles*

Answer 3

1. Draw the graph. y = 5.

2. Each side is twice 5. So 3 times twice 5 = 30 = perimeter.

3. Draw the picture. (6/8)12 = 9 = MN.

If you are trying to do these without drawing pictures, then you are making the problems harder to figure out.

Answer 4

1) Any horizontal line has a slope of zero. If the line crosses through (2,5), that means its y-intercept is 5, so in slope intercept form the equation of the line is y = 0x + 5

Answer 5

1)y=5
2)The side is 2MN =10 so the perimeter is 30
AB/MN=AC/CM
12/MN=8/6 so MN= 12*6/8= 9

Answer 6

1. y= 5
2. 7.5
3. 6