The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?

The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?

∵A（4，2），B （3，5）∴|AB|=10… (2 points) ∵ the vertex of an isosceles triangle is a, and the end point of its bottom is B, C | Ca | = 10, that is, C is on a circle with a center and a radius of 10 The equation is (x-4) 2 + (Y-2) 2 = 10 So the trajectory equation is (x-4) 2 + (Y-2) 2 = 10 (x ≠ 3,5) In order to improve the students' ability of analyzing and solving problems, we should take a (4,2) as the center of the circle, and take a 10 as the radius of the circle to remove (3,5) and (5, - 1) (14 points)

The vertex of isosceles triangle is a (4,2), and the bottom end is B (3,5). Find the trajectory equation of the other vertex C, and explain what its trajectory is?

∵A（4，2），B （3，5）∴|AB|=10… (2 points) ∵ the vertex of an isosceles triangle is a, and the end point of its bottom is B, C | Ca | = 10, that is, C is on a circle with a center and a radius of 10 The equation is (x-4) 2 + (Y-2) 2 = 10 A, B and C can't be collinear

What is the area of the triangle ABC enclosed by three points a (- 3,6), B (- 1, - 1) and C (4,2) in known coordinates

Similar problems can be done like this: first select two points randomly, find out the distance between the two points (set as l), and then find out the straight line of the two points. Then use the formula to find out the distance from another point to the straight line (set as d), and the area is 1 / 2LD. In addition, you can also build a triangle, and subtract the small triangle from the built triangle

Judge the shape of the triangle with three vertices a (1, - 1), B (2,1), C (- 1, - 1)

Obtuse triangle. You can find these three points on the coordinate axis and connect them

Given the coordinates of the three vertices of the triangle, try to judge the shape of the triangle
（1）A(1,2)B(1,4)C(-6，-4)
(2)E(4,3)F(1,2)G(3,-4)
3Q~

Idea: use the distance formula between two points to find the length of AB, AC, BC, and then use the cosine theorem to judge the shape of the triangle. (1) AB & # 178; = (1-1) &# 178; + (2-4) &# 178; = 4; AC & # 178; = (1 + 6) &# 178; + (2 + 4) &# 178; = 85; BC & # 178; = (1 + 6) &# 178; + (4 + 4) &# 178; = 113, if a

If the intersection of the three heights of a triangle is exactly one vertex of the triangle, then the triangle is ()
A. Acute triangle B. obtuse triangle C. right triangle D. indeterminate

A. For acute triangle, the intersection of the three high lines is in the triangle, so it is wrong; for B and obtuse triangle, the three high lines will not intersect at a vertex, so it is wrong; for C, the vertex of the right angle of the right triangle is exactly the intersection of the three high lines, so it can be concluded that the triangle is a right triangle, so it is correct; for D, it can be determined that C is correct, so it is wrong

If the intersection of the three heights of a triangle falls on a vertex, what is its shape______ ．

∵ the intersection of the three heights of a triangle falls on a vertex of the triangle, ∵ the triangle is a right triangle

If the intersection of the three heights of a triangle is exactly one vertex of the triangle, then the triangle is ()
A. Acute triangle B. obtuse triangle C. right triangle D. indeterminate

A. For acute triangle, the intersection of the three high lines is in the triangle, so it is wrong; for B and obtuse triangle, the three high lines will not intersect at a vertex, so it is wrong; for C, the vertex of the right angle of the right triangle is exactly the intersection of the three high lines, so it can be concluded that the triangle is a right triangle, so it is correct; for D, it can be determined that C is correct, so it is wrong

If the intersection of the three heights of a triangle is exactly one vertex of the triangle, then the triangle is ()
A. Acute triangle B. obtuse triangle C. right triangle D. indeterminate

A. For acute triangle, the intersection of the three high lines is in the triangle, so it is wrong; for B and obtuse triangle, the three high lines will not intersect at a vertex, so it is wrong; for C, the vertex of the right angle of the right triangle is exactly the intersection of the three high lines, so it can be concluded that the triangle is a right triangle, so it is correct; for D, it can be determined that C is correct, so it is wrong

The intersection of the three heights of a triangle is exactly one vertex of the triangle,

Right triangle
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