On a number line, the coordinate of A is -18 and that of B is 18. C is a point on AB such that AC:CB = 4:5. What is the coordinate of C?
with solution pls... tnx...
Did you make a sketch showing C somewhere between A and B ?
Mark the position of C with x
then AC =x-(-18) = x+18
and CB = 18-x
then (x+18)/(18-x) = 4/5
cross-multiply
5x + 90 = 72 - 4x
9x = -18
x = -2
so C is at -2
check by counting.
To find the coordinate of point C on the number line, we need to understand the given information and use it to calculate the position of point C.
Given:
Coordinate of point A = -18
Coordinate of point B = 18
AC:CB = 4:5
Step 1: Calculate the distance between point A and point B.
To find the distance between two points on a number line, we subtract the smaller coordinate from the larger coordinate. In this case, the distance between A and B is:
Distance AB = |coordinate of B - coordinate of A|
Distance AB = |18 - (-18)|
Distance AB = |18 + 18|
Distance AB = 36
Step 2: Divide the distance between A and B based on the ratio AC:CB.
The ratio AC:CB is given as 4:5, which means the total distance between points A and B will be divided into 4 parts for point A and 5 parts for point B. Therefore, each part will represent a fraction of the total distance.
Step 3: Calculate the fraction of the distance for point A (AC) and point B (CB).
The fraction for point A (AC) is given as 4/9 (since 4 parts out of 9 total parts)
The fraction for point B (CB) is given as 5/9 (since 5 parts out of 9 total parts)
Step 4: Calculate the distance of point C from point A.
To find the distance of point C from point A, we multiply the fraction for AC by the distance between A and B. Therefore:
Distance AC = Fraction AC * Distance AB
Distance AC = (4/9) * 36
Distance AC = 16
Step 5: Find the coordinate of point C.
To find the coordinate of point C, we add the distance AC to the coordinate of A. Therefore:
Coordinate of C = Coordinate of A + Distance AC
Coordinate of C = -18 + 16
Coordinate of C = -2
Therefore, the coordinate of point C is -2.
In conclusion, the coordinate of point C is -2.