Advertisements
Advertisements
प्रश्न
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Advertisements
उत्तर
PQ = `sqrt((5 - 0)^2 + (10 - 5)^2`
= `sqrt(25+25)`
= `sqrt(50)`
= 5`sqrt(2)`
QR = `sqrt((6 - 5)^2 + (3 - 10)^2`
= `sqrt(1+49)`
= `sqrt(50)`
= 5`sqrt(2)`
RP = `sqrt((0 - 6)^2 + (5 - 3)^2`
= `sqrt(36+4)`
= `sqrt(40)`
= 2`sqrt(10)`
Since, PQ = QR, ΔPQR is an isosceles triangle.
APPEARS IN
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
The distance between the points (0, 5) and (–3, 1) is ______.
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.
