What are the coordinates of the point on the directed line segment from (5, -5)(5,−5) to (7, 7)(7,7) that partitions the segment into a ratio of 3 to 1?

The coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is (6.5, 4)

Step-by-step explanation:

Here we have the points on the line given as

(5, -5)  and  (7, 7)

Therefore to the distance between the x and y coordinates are;

x-coordinate difference,  7 - 5 = 2 and

y-coordinate difference,  7 - (-5) = 12 and

The required ratio is 3:1, that is 3 portions on one side and 1 portion on the other.

Therefore, the total portion of the line is 3 + 1 = 4

So we divide each of the differences between x and y by 3/4 and add it to the coordinate of the first point on the line as follows

x-coordinate difference × 3/4 = 2×3/4 =1.5

y-coordinate difference × 3/4 = 12×3/4 = 9

Therefore, the coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is

x-coordinate = 5 + 1.5 = 6.5

y-coordinate = -5 + 9 = 4

or (6.5, 4).

its an acute right triangle

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752