Advertisements
Advertisements
प्रश्न
∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Using distance formula,
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
We can find,
AB = `sqrt((2 + 2)^2 + 0) = sqrt(16)` = 4
BC = `sqrt((0 - 2)^2 + (2 - 0)^2) = sqrt(8) = 2sqrt(2)`
CA = `sqrt((-2 - 0)^2 + (0 - 2)^2) = sqrt(8) = 2sqrt(2)`
DE = `sqrt((4 + 4)^2 + 0) = sqrt(64)` = 8
EF = `sqrt((0 - 4)^2 + (4 - 0)^2) = sqrt(32) = 4sqrt(2)`
FD = `sqrt((-4 - 0)^2 + (0 - 4)^2) = sqrt(32) = 4sqrt(2)`
∴ `("AB")/("DE") = ("BC")/("EF") = ("CA")/("FD") = 1/2`
⇒ ΔABC ∼ ΔDEF
Hence, triangle ABC and DEF are similar.
APPEARS IN
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
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 the distance between the points
A(-6,-4) and B(9,-12)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Find the distances between the following point.
A(a, 0), B(0, a)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Find the distance of the following point from the origin :
(8 , 15)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
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).
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`
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
