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"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 4
Thoughts and insights
1. The necessary and sufficient condition for two straight lines l1 and l2 to be vertical is that the product of their slopes is -1. Is this correct?
Tip: Incorrect. When the slopes of the two straight lines l1 and l2 do not exist, then when the two straight lines are perpendicular, it cannot be deduced that the product of their slopes is equal to -1.
2. When applying the distance formula from a point to a straight line, what form should the straight line equation be put into?
Tip: Convert the equation of the straight line into a general form.
1. The straight line x+ay+1=0 and 2x-y+3=0 are parallel, then a is ()
A. -1/2 B. 1/2
C. 2D. -2
2. It is known that the distance from point (a, 2) (a>0) to straight line l: x-y+3=0 is 1, then a is equal to ()
A. √2B. 2-√2
C. √2-1 D. √2+1
3． If three straight lines y=2x, x+y=3, mx+ny+5=0 intersect at the same point, then point (m, n) may be ()
A. (1,-3) B. (3,-1)
C. (-3,1) D. (-1,3)
4. The angle between the straight line y=2 and the straight line x+y-2=0 is ________.
Analysis: The inclination angle of the straight line x+y-2=0 is 3/4π
The angle required is |π-3π/4|=π/4
5. If the straight line ax+2y-6=0 is parallel to x+(a-1)y-(a2-1)=0, then the distance between them is equal to ________.
1. When explaining the positional relationship, use the relationship of A1/A2, B1/B2, C1/C2 to examine it. It is not a necessary or sufficient relationship. For example, the two straight lines represented by 2x-1=0 and 3x-4=0 are parallel, but it cannot be used as A1/ A2=B1/B2≠C1/C2 to illustrate.
2. "k1＝k2⇔l1∥l2" and "k1k2＝-1⇔l1⊥l2" are based on the premise that both k1 and k2 exist, and the intercept of the two straight lines on the y-axis b1≠b2, k1＝k2, Only l1∥l2.
3． When discussing the positional relationship between two straight lines, the geometric significance of using the slope-intercept form of the straight line equation is obvious, but attention should be paid to the situation where the slope does not exist.
Given two straight lines l1: ax-by+4=0 and l2: (a-1)x+y+b=0, find the values of a and b that satisfy the following conditions.
(1)l1⊥l2, and l1 passes the point (-3,-1);
(2)l1∥l2, and the distance from the coordinate origin to these two straight lines is equal.
distance problem
1. The formulas for the distance from a point to a straight line and the formula for the distance between two parallel lines are commonly used formulas and should be mastered proficiently.
2. The distance from a point to several special straight lines
(1) The distance d from point P (x0, y0) to the x-axis = |y0|.
(2) The distance d from point P (x0, y0) to the y-axis = |x0|.
Symmetry problem
1.Central symmetry
(1) If points M (x1, y1) and N (x, y) are symmetrical about P (a, b), then x=2a-x1, y=2b-y1 can be obtained from the midpoint coordinate formula
(2) The main method of making a straight line symmetrical about a point is: take two points on a known straight line, use the midpoint coordinate formula to find the two-point coordinates of their symmetry about the known point, and then use the two-point formula to find the equation of the straight line , or find a symmetry point, and then use l1∥l2 to obtain the equation of the straight line from the point-slope formula.
2. Axisymmetric
(1) Point symmetry about a straight line If two points P1 (x1, y1) and P2 (x2, y2) are symmetric about the straight line l: Ax+By+C=0, then the midpoint of the line segment P1P2 is on the symmetry axis l, and the straight line connecting P1P2 Perpendicular to the axis of symmetry l, the coordinates (x2, y2) of point P2 that is symmetrical about point P1 about l can be obtained from the system of equations (where B≠0, x1≠x2).
(2) The symmetry of a straight line about a straight line
Such problems are generally solved by converting them into symmetry points about a straight line. If it is known that the straight line l1 intersects with the symmetry axis l, the intersection point must be on the straight line l2 that is symmetrical with l1, and then find the symmetry of any known point P1 on l1 Point P2 that is symmetrical about axis l, then the straight line passing through the intersection point and point P2 is l2; if it is known that straight line l1 is parallel to the symmetry axis l, then the straight line symmetrical to l1 and the distance from l1 to straight line l are equal. The parallel straight line system and the two The distance between two parallel lines can be used to find the symmetric straight line of l1.
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"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 3:
"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 3 [Course Standard Requirements] 1. Can determine whether two straight lines are parallel or perpendicular based on their slope. 2. Can find the equation of a straight line based on whether two straight lines are parallel or perpendicular. 【Core scan】 1． Use two parallel lines...
"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 2:
"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware 2 Basic Review 1. Determining whether two straight lines are parallel or perpendicular (1) Suppose the slopes of the two straight lines l1 and l2 are k1 and k2 respectively, and the inclination angles are 1 and 2 respectively. Then when l1∥l2, 1=2, thus l1∥l2_. .
"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware:
"The Positional Relationship of Two Straight Lines" Parallel Lines and Intersecting Lines PPT Courseware Return to Textbook 1. If two straight lines have one and only one common point, then the two straight lines intersect; if there is no common point, then the two straight lines are parallel; if there are countless common points, then The two straight lines coincide. The straight line equation (1) passes...