问题1.在以下每个给定的点上找到具有顶点的三角形区域:
(i)(1、0),(6、0),(4、3)
(ii)(2、7),(1、1),(10、8)
(iii)(–2,–3),(3,2),(–1,–8)
解决方案:
(i) (1, 0), (6, 0), (4, 3)
(ii) (2, 7), (1, 1), (10, 8)
(iii) (–2, –3), (3, 2), (–1, –8)
问题2。证明点A(a,b + c),B(b,c + a),C(c,a + b)是共线的。
解决方案:
If the area of the triangle is equal to zero then the points are collinear.
For example:- Area of triangle = 0
问题3.如果三角形的面积是4平方单位,并且顶点是
(i)(k,0),(4,0),(0,2)
(ii)(-2,0),(0,4),(0,k)
解决方案:
(i) (k, 0), (4, 0), (0, 2)
Given: Area of triangle = ±4 sq. units
i.e.
(ii) (-2, 0), (0, 4), (0, k)
问题4。(i)使用行列式找到线连接(1,2)和(3,6)的方程。
(ii)使用行列式找到线连接(3,1)和(9,3)的方程式。
解决方案:
(i) Find equation of line joining (1, 2) and (3, 6) using determinants.
Let us assume,
A(x, y) be any vertex of a triangle
All points are on one line (collinear) if the area of triangle is zero.
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants.
Let us assume,
A(x, y) be any vertex of a triangle
All points are on one line (collinear) if the area of triangle is zero.
问题5.如果三角形的面积是35平方单位,且顶点分别为(2,– 6),(5,4)和(k,4)。那么k是
(A)12(B)–2(C)–12,–2(D)12,–2
解决方案:
(D) is the correct option.
As: