0) 7. Line AB has the endpoints A(8, 8) and B(4, 2)
What are the x- and y-coordinates of point
C that partitions AB at a 1 : 5 ratio.
C is at (
*
)*
C
D
+
et

The coordinates of C(22/3, 7)

Step-by-step explanation:

Partitioning between two points A and B in the ratio a:b.

The x-coordinate of the point of partition C is found at

XC = XA*(b/(a+b)+XB(a/(a+b) (1)

Similarly, the x-coordinate of the point of partition is found at

YC = YA*(b/(a+b)+YB(a/(a+b)(2)

Given A(8,8), B(4,2), partition ratio of A:B = 1:5,

substitute in (1)

XC = 8*5/6+4*1/6 = 44/6 = 22/3

YC = 8*5/6 + 2*1/6 = 42/6 = 7

The coordinates of C(22/3, 7)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions