What are the coordinates of the point on the directed line segment from (- 3, - 9) to (4, 5) that partitions the segment into a
1 answer:
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First exercise:
a. The first prime numbers are 2,3,5,7,11,... So, the greatest prime interger between 4 and 9 is 7. A = 7.
b. Since the number line's growing direction is rightwards, going to the left means to decrease. So, point E is 4 less than point A, i.e. 7-4 = 3. E = 3.
c. The additive inverse of a number is another number
such that
. So, we're looking form a number such that
, and thus O = - 3.
d. This point looks a bit ambiguous to me honestly. We know that IO = 2, which I presume means that the points I and O are two units apart, but we're not told if I is two units left or right with respect to O. To solve this issue, I'm assuming that IO implies that I sits before O, and so I is two units left with respect to O. As we said in point a., two units left means two less, so we have I = -3-2 = -5. At this point, point L is halfway between -5 and -3, and thus L = - 4.
e. The sum of the coordinates of A and E is 7 + 3 = 10. Half that sum is 5, so M = 5.
In the attached image, you can see the number line filled with the points asked by the exercise.
Second exercise:
All the requests can be written as an equation in which we look for the values of x. Below you find the equation and the solutions.
A little side note: I've honestly never met the expression "subtract A to B", but always "subtract A from B". I assumed they mean the same thing, but if anybody thinks I'm wrong please let me know! (I'm not a native speaker, so I can only refer to the math I met during my studies).
to get the equation for any straight line, all we need is two points from it, so hmmm say from this table let's use (2,0) and (6,-8)