For a trapezoid, if the bottom and height remain unchanged, the area of the trapezoid will increase by 1.2 square meters if the top and bottom increase by 0.6 meters; if the top and bottom remain unchanged, the height will decrease by 0.8 meters, and the area of the trapezoid will decrease by 2 square meters?

For a trapezoid, if the bottom and height remain unchanged, the area of the trapezoid will increase by 1.2 square meters if the top and bottom increase by 0.6 meters; if the top and bottom remain unchanged, the height will decrease by 0.8 meters, and the area of the trapezoid will decrease by 2 square meters?

The original area is 10 square meters. First set the height as h, 0.6h * 1 / 2 = 1.2, H = 4, set the upper bottom and lower bottom as m, m * 0.8 * 1 / 2 = 2, M = 5, so the area is 4 * 5 * 1 / 2 = 10 square meters

For a trapezoid, if the bottom and height remain unchanged, and the upper bottom increases by 0.6 meters, the area of the trapezoid will increase by 1.2 square meters?

Let X be the upper base, y be the lower base, and H be the height
(x + y) H / 2 + 1.2 = (x + y + 0.6) H / 2, simplification
(x+y)h+2.4=(x+y)h+0.6h
The solution is h = 4

A trapezoid has an area of 1.2 square meters, a height of 0.6 meters, and a top bottom length of 1.8 meters. How long is the bottom of this trapezoid?

1.2 × 2 △ 0.6-1.8 = 2.2 (m)
(1.8+x)×0.6÷2=1.2
x=2.2

In plane coordinate system, does the formula of 3-point coordinate offset after the triangle area is doubled
If the three-point coordinates of a triangle are known in the XY plane, when the area of the triangle is doubled, what is the new three-point coordinates and what is the offset from the original coordinates?

There are formulas in theory, but they are so complicated that you don't want to use them at all... Let's do it step by step
First find two points and find the distance between them
Next, apply the point to line formula to calculate the distance from the third point to the line (that is, the height of the triangle)
So the area is 1 / 2 of the product of two distances
Can you understand that?

Triangle in the coordinate system area formula, I remember what is the horizontal height, the best graph

S = 0.5 * horizontal height * vertical height

Coordinate system, triangle area~
The three vertices of the triangle are (- 4,1) (3,4) (5, - 3)
Triangle area. Urgent need to answer ~ thank you!

Draw a picture. The area of a triangle is equal to the area of a rectangle minus the area of three right triangles
Triangle area = (5 + 4) x (4 + 3) - 1 / 2 x9 X4 - 1 / 2 x 2x7 - 1 / 2 x3x7 = 27.5

What are the operational properties of determinants? They are mainly used for simplification, such as row to row exchange and value invariance

(1) The value of a determinant is the same when it is exchanged between rows and columns; (2) when two rows (columns) are exchanged, the value of the determinant changes sign; (3) if a row (column) has a common factor, the common factor can be put forward; (4) if each element of a row (column) is the sum of two numbers, the determinant can be divided into the sum of two determinants; (5) if K times of a row (column) is added to another row (column), the value will not change

Use determinant properties to calculate the following determinants
x y x+y
y x+y x
x+y x y

C1 + C2 + C3 column 2,3 added to column 1
2(x+y) y x+y
2(x+y) x+y x
2(x+y) x y
r2-r1,r3-r1
2(x+y) y x+y
0 x -y
0 x-y -x
=2(x+y)[-x^2+y(x-y)]
=-2(x+y)(x^2-xy+y^2)

By using the property of determinant, change the following determinant into upper triangular form, and find its value: 1 1 - 1 1 - 1 1 1 - 1 1 1 - 1 1

RI + R1, I = 2,3,4 (all lines plus the first line)
1 1 1 1
0 2 2 2
0 0 2 2
0 0 0 2
= 8.

What are the properties of determinant

1. The determinant is equal to its transposed determinant
2. The common factor of a row element in the determinant can be referred to the outside of the determinant symbol. In other words, if you multiply the determinant by a number, you can multiply the number to a row of the determinant
3. If all elements in one row of determinant are zero, the value of determinant is zero
4. Exchange two lines of determinant, determinant only changes sign
5. If two lines in the determinant are exactly the same, then the value of the determinant is zero
6. If a determinant has two lines of proportional elements, then the determinant is equal to zero
7. Multiply the elements of one row of determinant by the same number and add them to the corresponding elements of another row. The determinant remains unchanged