Given the coordinates of A and C ad (-6,-5) and (6,7) respectively and point B is on AC. Find the coordinates of B such that the ratio of AB to BC is 3:1
I just need an assurance because I got the answer (30,31). And I started to feel weird if my answer is correct? Because its too big
You know that C is between A and B. How can its coordinates be (30,31)? That's way off the chart! Did you actually plot the points? !?!
You were correct to feel weird. Always do a sanity check when you get an answer. See whether it makes any sense.
AB:BC = 3:1 means that C is 3/4 of the way from A to B.
For the x-coordinate, 3/4 of the way from -6 to 6 is 3
For the y-coordinate, 3/4 of the way from -5 to 7 is 4
So, B = (3,4)
Too bad you didn't show any of your work ...
I will use that! Thank you very much for the advise!
What I did is
X = X1 + k (X2-X1)
= -6 + 3 (6+6)
= -6 + 3 (12)
= -6 + 36
= 30
Same procedure with the other side. Thank you very much! I just can't understand my teacher completely and having a trouble researching in YouTube and textbook.
I see I made a typo. It should have read
AB:BC = 3:1 means that B is 3/4 of the way from A to C.
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To find the coordinates of point B on line AC such that the ratio of AB to BC is 3:1, we can use the concept of section formula.
Let's assume the coordinates of point B as (x, y). The ratio of AB to BC is 3:1, which means that the distance between A and B is three times the distance between B and C.
Using the distance formula, we can calculate the distances AB and BC:
AB = √((x2 - x1)² + (y2 - y1)²) [where (x1, y1) = (-6, -5) and (x2, y2) = (x, y)]
BC = √((x2 - x1)² + (y2 - y1)²) [where (x1, y1) = (6, 7) and (x2, y2) = (x, y)]
Since AB is three times BC, we can write the equation:
√((x - (-6))² + (y - (-5))²) = 3 * √((x - 6)² + (y - 7)²)
Simplifying this equation:
√((x + 6)² + (y + 5)²) = 3 * √((x - 6)² + (y - 7)²)
Squaring both sides:
(x + 6)² + (y + 5)² = 9 * ((x - 6)² + (y - 7)²)
Expanding and simplifying:
x² + 12x + 36 + y² + 10y + 25 = 9x² - 108x + 324 + 9y² - 126y + 441
Rearranging terms and combining like terms:
8x² - 120x + 8y² - 136y - 4 = 0
This equation represents an ellipse, not a line. Therefore, there is no single point B that satisfies the given condition. It is possible that you made an error in your calculations, which resulted in the seemingly large coordinates (30, 31). I recommend double-checking your calculations to determine the correct coordinates of point B.