Advertisements
Advertisements
प्रश्न
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
Advertisements
उत्तर
By distance formula,
PQ = `sqrt(bb((x^2 - x_1)^2) + (y_2 - y_1)^2`
= `sqrt(bb(0 - (-5)^2) + bb(3 - (-7)^2))`
= `sqrt(bb((5)^2) + bb((10)^2))`
= `sqrt(bb25 + bb100)`
= `sqrt(125)`
= `5sqrt(5)`
APPEARS IN
संबंधित प्रश्न
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
A line segment of length 10 units has one end at A (-4 , 3). If the ordinate of te othyer end B is 9 , find the abscissa of this end.
Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.
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.
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
Find distance CD where C(–3a, a), D(a, –2a).
Show that the points (2, 0), (–2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
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.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
