Fun math trivia problems!?

Question

1.determine the value of r so that a line through the points with the coordinates )r,4) and (-2,3) has slope 1/4.

2. what is the lehgnth of a line with coordinates (-4,-3) and (4,3).

3. Find the midpoint of the segment with endpoints A(-6,4) and C(4,-6)

4. WHat is the least number of thumtacks that must be used to tack up 12 regular pictures, all the same siz,so that they can all be seen? Assume each corner of each picture is tacked. (A tack can be in the corner of more than one picture)

Answer 1

1)
point 1 (x1, y1) = (r, 4)
point 2 (x2, y2) = (-2, 3)

slope (m) = rise / run

rise = y2 - y1 = 4 - 3 = 1
run = x2 - x1 = r - (-2) = 4
r + 2 = 4
r = 2

2) The rise is 6 (3 minus -3) and the run is 8 (4 minus -4), so if you use the pythagorean theorem (a² + b² = c²) you'll see that the distance is 10. You've essentially got a 3-4-5 triangle, but doubled to 6-8-10.

Line length is 10.

3) Midpoint is the average of the x and y coords.
xmid = (-6 + 4) / 2 = -2 / 2 = -1
ymid = (4 + -6) / 2 = -2 / 2 = -1

So the midpoint is (-1, -1)

4) You want them in as compact an arrangement as possible. Certainly choices like 1 x 12 or 2 x 6 are bad. Put them in a 3 x 4 grid. Now for each row and column you need one additional thumbtack.

For a 3 x 4 arrangement, you need 3+1 by 4+1 thumbtacks (4 x 5), for a total of 20 thumbtacks.

Answer 2

4. What is the least number of thumtacks that must be used to tack up 12 regular pictures, all the same siz,so that they can all be seen? Assume each corner of each picture is tacked. (A tack can be in the corner of more than one picture).

The answer is 20 tacks.

If you arrange the pictures in a 4 by 3 grid you can tack them up with 20 tacks. (The tacks would be in a 5 by 4 arrangement.)

Answer 3

1. To solve this problem, all we need is the slope formula

m = (y2 - y1) / (x2 - x1). Using (x1,y1) as (-2,3) and (x2, y2) as
(r, 4), noting m = 1/4, we get

1/4 = (4 - 3) / (r - (-2))
1/4 = 1 / [r + 2]

Cross multiplying,

r + 2 = 4, therefore r = 2.

2. To find the length of the line with endpoints (-4, -3) and (4, 3), we use the distance formula.

d = sqrt ( (x2 - x1)^2 + (y2 - y1)^2 )
d = sqrt ( [4 - (-4)]^2 + [3 - (-3)]^2 )
d = sqrt ( [8]^2 + [6]^2 )
d = sqrt (64 + 36) = sqrt (100) = 10

Therefore, the length is 10.

3. The midpoint M of two points is calculated by the following:
M = ( (x1 + x2)/2 , (y1 + y2)/2 )
M = ( (-6 + 4)/2 , (-6 + 4)/2 )
M = ( (-2/2) , (-2,2) )
M = (-1, -1)

Answer 4

2. the old right triangle ploy - 3 -4 -5 squared 9+16=25
distance 10

4. thumbtacks 26

Answer 5

1.
(3 - 4)/-(r + 2) = 1/4
r + 2 = 4
r = 2

2.
√(8^2 + 6^2) = 10

3.
P = (-1,-1)

4.
(4 + 1)(3 + 1) = 20

Answer 6

1) 2

2) 10

3) (-1,-1)

4) 20

Answer 7

2&7