Advertisements
Advertisements
Question
Find the area of the triangle whose vertices are: (–5, –1), (3, –5), (5, 2)
Solution
Area of the given triangle = `1/2 [-5 { (-5)- (4)} + 3(2-(-1)) + 5{-1 - (-5)}]`
`= 1/2{35 + 9 + 20}`
= 32 square units
APPEARS IN
RELATED QUESTIONS
The two opposite vertices of a square are (− 1, 2) and (3, 2). Find the coordinates of the other two vertices.
The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the following figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.
Find the area of a triangle whose vertices are
(a, c + a), (a, c) and (−a, c − a)
Show that the following sets of points are collinear.
(2, 5), (4, 6) and (8, 8)
Prove that the points (a, b), (a1, b1) and (a −a1, b −b1) are collinear if ab1 = a1b.
Prove that the points A(2, 4), b(2, 6) and (2 +`sqrt(3)` ,5) are the vertices of an equilateral triangle
Find the area of ΔABC whose vertices are:
A( 3,8) , B(-4,2) and C( 5, -1)
Find a relation between x and y, if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.
A field is in the shape of a right angled triangle whose base is 25 m and height 20 m. Find the cost of levelling the field at the rate of ₹ 45 per sq.m2
