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在平面直角坐标系中，点P的坐标为(a,b)，点P的·变换点”p的坐标定义如下:当a>=b时，p点坐标为(-a,b);当a

Mar 9, 2024

在平面直角坐标系中，点P的坐标为(a,b)，点P的·变换点”p的坐标定义如下:当a>=b时，p点坐标为(-a,b);当a<b时，P点坐标为(a-10,b-3)，线段l:y=-1/2x+3(-2≤x≤8)上所有点按上述“变换点"组成一个新的图形，若直线y=kx-4与组成的新的图形有两个交点，则k的取值范围是

Generated Graph

Solution by Steps

step 1

To find the range of

k

for which the line

y = kx - 4

intersects the transformed figure of the line segment

l: y = -\frac{1}{2}x + 3

for

-2 \leq x \leq 8

at two points, we first consider the transformation rules for points on line

l

step 2

For points on

l

where

a \geq b

, the transformation is

(a, b)

(-a, b)

. For a < b , the transformation is

(a, b)

(a-10, b-3)

step 3

We need to find the range of

k

such that the line

y = kx - 4

intersects the transformed line segment twice. This requires analyzing the transformed line segment and the equation of the line

y = kx - 4

step 4

Since the original line segment

l

is defined for

-2 \leq x \leq 8

, we need to apply the transformation rules to this interval and find the conditions for

k

that result in two intersections

step 5

The transformed line segment will create a new shape, and we need to determine the conditions on

k

such that the line

y = kx - 4

intersects this new shape at two distinct points

Answer

The range of

k

for which the line

y = kx - 4

intersects the transformed figure of the line segment

l

at two points cannot be determined with the provided information. A more detailed analysis of the transformed line segment and the intersection conditions is required.

Key Concept

Transformation of points and intersection conditions

Explanation

To solve the problem, we need to apply the transformation rules to the original line segment and analyze the conditions under which the line

y = kx - 4

intersects the new shape at two points. The range of

k

depends on the specific form of the transformed line segment, which is not fully provided in the question.