Advertisements
Advertisements
प्रश्न
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
उत्तर
A ≡ (2, 0) ≡ (x1, y1)
B ≡ (–2 , 0) ≡ (x2, y2)
C ≡ (0, 2) ≡ (x3, y3)
∴ ABC form a triangle.
AB = `sqrt ((x_2 - x_1)^2 + ("y"_2 - "y"_1)^2)`
= `sqrt ((-2-2)^2 + (0 - 0)^2)`
= `sqrt ((-4)^2 + 0)`
= `sqrt(16)`
= 4 units
AC = `sqrt ((x_3 - x_1)^2 + ("y"_3 - "y"_1)^2)`
= `sqrt ((0-2)^2 + (2 - 0)^2)`
= `sqrt ((-2)^2 + (2)^2)`
= `sqrt (4 + 4)`
= `sqrt(8)`
= `2sqrt(2)` units
BC = `sqrt ((x_3 - x_2)^2 + ("y"_3 - "y"_2)^2)`
= `sqrt ((0-(-2)^2) + (2 - 0)^2)`
= `sqrt ((0 + 2)^2 + (2 - 0)^2)`
= `sqrt ((2)^2 + (2)^2)`
= `sqrt(8)`
= `2sqrt(2)` units
So, if side AC and side BC are equal then the triangle is an isosceles triangle.
AB2 = BC2 + AC2
`(4)^2 = (2sqrt2)^2 + (2sqrt(2))^2`
16 = 8 + 8
16 = 16
So, it is a right-angle isosceles triangle.
APPEARS IN
संबंधित प्रश्न
If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
Find the distance between the following pair of points:
(-6, 7) and (-1, -5)
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
Find the distance of the following points from origin.
(5, 6)
Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).
Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)
The distance between the points A(0, 6) and B(0, -2) is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
Read the following passage:
|
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
|
Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
-
- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
