Given expression doesn't readily factorize; dilation of point (3,4) with center (2,0) and scale factor 2 results in (5,12); the equation of the line through (3,4) and (5,12) is y = 4x - 8.
To factorize the expression s3−9s2+s−9, we look for common factors and also patterns that might indicate a special product. Unfortunately, there doesn't seem to be a straightforward factorization for this expression, and it likely involves complex or irrational roots. For now, we won't factorize this expression as it doesn't factor over the integers.
In the case of dilation, the coordinates of point C (3,4) when dilated with a center of (2,0) and a scale factor of 2, will be found by increasing the distance of point C from the center by two times. The x-coordinate will increase by 2 times (3-2) which is 2, so 3 + 2 = 5. The y-coordinate will increase by 2 times 4, which is 8, so 4 + 8 = 12. Therefore, the coordinates of the dilated image of point C are (5,12).
The equation of the line passing through the original point C (3,4) and its dilated image (5,12) can be found using the slope formula. The slope, m, is the change in y over the change in x, which in this case is (12 - 4) / (5 - 3) = 8/2 = 4. Using the point-slope formula, the equation of the line is y - 4 = 4(x - 3), which simplifies to y = 4x - 8.
The probable question may be:
Given the expression s^3−9s^2+s−9, factorize it completely.
Coordinate Transformation:
Point C in a coordinate system has coordinates (3,4). If triangle ABC is dilated with center (2,0) and a scale factor of 2, find the coordinates of the image of point C after dilation.
Equation of a Line:
Considering a line passing through the original point C(3,4) and its dilated image, write an equation for the line containing all possible images of point C after the dilation process.
Additional Information:
In mathematics, factoring is a fundamental skill used to simplify expressions. Dilations involve enlarging or reducing figures by a scale factor while maintaining their shape. The equation of a line is a crucial concept in coordinate geometry, providing a way to express the relationship between points on a plane. These concepts are essential in various mathematical applications, from algebraic simplifications to geometric transformations.