If four points A 5,0 B 1,0 C 3,3 D a,3 are concomplete, find the value of a

If four points a(5,0), b(-1,0), c(-3,3), and d(a,3) are concomplete, find the value of a. Yes, the circle formed by ABC three points, then the intersection of the center of the circle on the perpendicular line of ab, ac, and bc has the perpendicular line of ab x=2, so let the coordinates of the center of the circle o(2,m) and ao=bo=co, so (5-2) 0 5+(0-m) 0 5=(-3-2) 0 5+(3-m) 0 5 get m=25 6 radius r 0 5=26 and 13 36, so the equation for the circle o: (x-2) 0 5+(y-25 6) 0 5=949 26 will be d point y=3 brings in the equation (x-2) 0 5=5, so there is x1=7 or x2=-3, that is, a has two values of -3 or 7, and d1 (-3, 3) coincides with point c, which does not meet the topic, so the community and d2 (7, 3) conforms to the topic, so a=7

Since A and B are both on the X axis, then the center of the circle should be on the perpendicular line of AB, and the perpendicular line is X=2;In addition, cd ab is on the same circle, so c and d are also symmetrical with respect to x=2, so we can get a=7

The formula for the distance between two points: for example, a(x1,y1), b(x2,y2), then the length of ab = [x1-x2) 2 + y1-y2) 2] Let the center of the circle o(m,n) then, oa=ob=oc=od, oa 2=ob 2=oc 2=od 2oa= [(m-5) 2 + n-0) 2]= [(m-5) 2 + n 2]ob= [(m+1) 2 + n-0) 2]= [(m+1) 2 + n 2]0c= [(m+3) 2 + n-3) 2] od= [(m+a) 2 + n-3) 2](m-5) 2 + n 2=(m+1) 2 + n 2=(m+3) 2 + n-3) 2=(m-a) 2 + n-3) 2m=2,n=25 6a=7 or a=-3 Since there is c(-3,3), when a=-3 d(-3,3) overlaps with point c(-3,3), so, a=7

AB coincides with the X-axis, CD X-axis.

ab//cd

The straight line x=2 bisects ab perpendicularly and is parallel to the y-axis.

The center of the circle is on the straight line x=2.

The circle has only two intersections with y=3, and the center of the circle is on the perpendicular bisector of cd.

The collapse point c and the point d are symmetrical with respect to the base line x = 2.

a=2*2-（-3）=7

It is easy to get the coordinates of the center of the circle (4,3) from the three points of ABC, and the radius of the hand is 2

Referring to the calendar 5-4) only potato search 2 + (m-3) 2 = 2 2

m=3+-root number 3

Summary. 1) If a quadrilateral is a parallelogram, then the two sets of opposite sides of this quadrilateral are equal. (2) If a quadrilateral is a parallelogram, then the two sets of diagonal diagonals of the quadrilateral are equal.

It is simply stated as "the two sets of diagonal angles of a parallelogram are equal") (3) If a quadrilateral is a parallelogram, then the adjacent angles of this quadrilateral complement each other. (4) The height of the parallel is equal between two parallel lines. (5) If a quadrilateral is a parallelogram, then the two diagonals of the quadrilateral are bisected from each other.

4.If the points a(1,2),b(5,0),c(3,4),d(-1,6) are known, then the quadrilateral is a parallelogram.

A group of quadrilaterals with two opposing sides parallel to each other is called a parallelogram. Parallelograms are generally named with the name of the figure plus four vertices in sequence.

1) If a quadrilateral is a parallelogram, then the two sets of opposite sides of this quadrilateral are equal. (2) If a quadrilateral is a parallelogram, then the two sets of diagonal diagonals of the quadrilateral are equal. It is simply stated as "the two sets of diagonal angles of a parallelogram are equal") (3) If a quadrilateral is a parallelogram, then the adjacent angles of this quadrilateral complement each other.

Bond combustion is simply described as "the adjacent angles of the parallelogram complement each other") (4) The parallel height is equal between two parallel lines. (5) If a quadrilateral is a parallelogram, then the two diagonals of the quadrilateral are bisected from each other.

【Solve Answer】When a=0, a(-2,5), b(1,9), and c(4,13) are collinear.

Three-point collinear means that three points are on the same straight line. The solution idea: if A, B, and C are collinear, the slopes of the AC line and the BC line must be equal and the intercept must be equal.

So we can solve it in the following steps.

1. Use the two-point square block to find the AC linear equation and the BC linear equation respectively

AC line: 8x-(6-a)y-13a+46=0

BC line: (4-a) x-3y+2a+23=0

2. According to the coincidence condition of the two straight lines

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3. Solve the above equation to obtain the value of a.

Solve Process

[Knowledge points of this question].

1. Two-point linear equation.

If the coordinates of point A (x1, y1) and point b (x2, y2) are known, then there is

2. Three-point collinear.

The sufficient and necessary conditions for three points to be collinearal in the same straight line are:

Let the equation for the circle be (x, a) y b) =r, and substitute a(5,0)b(-1,0)c(-3,3) into the equation to form the equation respectively, and the values of a, b, and r can be obtained.

Then you can find the equation of the circle, so that the equation y=3, and solve the equation to find x, and the value of x is the value of a!

AB coincides with the X-axis, CD X-axis.

ab//cd

The straight line x=2 bisects ab perpendicularly and is parallel to the y-axis.

The center of the circle is on the straight line x=2.

The circle has and can only have two intersections with the line y=3, and the center of the circle is symmetrical with respect to the line x=2 on the perpendicular bisector of cd with point c and point d.

a=2*2-（-3）=7

Answer: Since a, b, c, and d are all in a circle, the coordinates of the four points are substituted into the equation x +y + dx + ey+f=0 of the circle

5²+5d+f=0...1

a²+ad+f=0...2

3）²+3²-3d+3e+f=0...37²+3²+7d+3e+f=0...4

Solution: d=-4, f=-5, substitute 2 formula: a Lao Xukai -4a-5 = 0. Solution: a1=-1, a2=5 (known points, omitted).

That is, the value of a: a1=-1.

Solution: Let the coordinates of this circle be (x, y), then the equation for the perpendicular bisector of the line segment ac is:

x--5) 2+y 2=(x+3) 2+(y--3) 2, i.e.: 16x--6y--7=0 (1).

In the same way, the equation for the perpendicular bisector of the Rotten Song segment cd is:

x=2 (2)

From (1), (2): The coordinates of the circle are (2,25 6), because the point (a, 0) is on this circle, so (a--5) 2+(0--0) 2=(a+3) 2+(0--3) 2

a^2--10a+25=a^2+9a+9+919a=7a=7/19.

Since a and b are both on the x-axis, then the center of the circle should be on the perpendicular line of ab, and the perpendicular line of ab is x=2;In addition, cd ab is on the same circle, so c and d are also symmetrical with respect to x=2, so we can get a=7

Let's draw a picture yourself, it's very intuitive.

d（a，3）?A circle y is the same, x should be the same, didn't you write c(-3,3), how can d's y also be 3, oh, I said it wrong.

There is also symmetry d(