In the plane rectangular coordinate system, the image of a linear function passes through the point a (0,4) B (2,0) (2) to translate the line AB to the left, if the translated line intersects the X axis At point C, and AC = BC, find the coordinates of point C and the expression of the line after translation

In the plane rectangular coordinate system, the image of a linear function passes through the point a (0,4) B (2,0) (2) to translate the line AB to the left, if the translated line intersects the X axis At point C, and AC = BC, find the coordinates of point C and the expression of the line after translation

Let the analytic expression before translation be Y1 = K1X + B1, take the point a (0,4) B (2,0) into K1 = - 2, B1 = 4. Then the analytic expression before translation is y = - 2x + 4 as the vertical bisector CD of line AB, intersecting the x-axis at point C, and the perpendicular foot is d. then point C satisfies the meaning of the problem. It is easy to get △ BCD ∽ Bao, then BC: ab = BD: OB ∵ OA = 4, OB = 2 ∵ AB = 2, radical sign 5 ∵ Bo = root

If the line L moves three units to the left along the x-axis, and then one unit up along the y-axis, and returns to the original position, then the slope of the line l will decrease______ ．

Let the equation of the line l be y = KX + B, then y = KX + B translates 3 units to the left along the X axis, y = K (x + 3) + B translates 1 unit up along the Y axis, y = KX + 3K + B + 1. Because it returns to the original position after two translation transformations, there must be 3K + B + 1 = B, and the solution is k = -13

If the line L moves 3 units in the negative direction of x-axis and 1 unit in the positive direction of y-axis, then it returns to its original position, then the slope of line L is ()
A. −13B. -3C. 13D. 3

Let the equation of the straight line l be y = KX + B. according to the translation of the meaning of the problem, we can get y = K (x + 3) + B + 1, that is, y = KX + 3K + B + 1, then KX + B = KX + 3K + B + 1, and the solution is k = - 13

If the line L moves three units to the left along the x-axis, and then one unit up along the y-axis, and returns to the original position, then the slope of the line l will decrease______ ．

Let the equation of the line l be y = KX + B, then y = KX + B translates 3 units to the left along the X axis, y = K (x + 3) + B translates 1 unit up along the Y axis, y = KX + 3K + B + 1. Because it returns to the original position after two translation transformations, there must be 3K + B + 1 = B, and the solution is k = -13