English
Maharashtra State BoardSSC (English Medium) 10th Standard

Find the Co-ordinates of the Centroid of the δ Pqr, Whose Vertices Are P(3, –5), Q(4, 3) and R(11, –4)

Advertisements
Advertisements

Question

Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4) 

Sum
Advertisements

Solution

Co- ordinates of the centroid of triangle PQR are 

`((3+4+11)/(3),(-5+3-4)/(3))`

`=(6,-2)`

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (July) Set 1

APPEARS IN

RELATED QUESTIONS

Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are `2/3` of the corresponding sides of the first triangle. Give the justification of the construction.

 


Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose side are `1 1/2` times the corresponding sides of the isosceles triangle.

Give the justification of the construction


Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. the construct another triangle whose sides are `5/3` times the corresponding sides of the given triangle. Give the justification of the construction.


Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.


Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.


Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.


Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.


Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.


Draw a ∆ABC in which AB = 4 cm, BC = 5 cm and AC = 6 cm. Then construct another triangle whose sides are\[\frac{3}{5}\]  of the corresponding sides of ∆ABC ?


Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.


If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.


If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.


Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SHSV = 53 then draw Δ SVU.


Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.


______ number of tangents can be drawn to a circle from the point on the circle.


∆ABC ∼ ∆AQR. `(AB)/(AQ) = 7/5`, then which of the following option is true?


Draw seg AB of length 9 cm and divide it in the ratio 3 : 2.


Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC.


ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(AM)/(HA) = 7/5`, then construct ΔAMT and ΔAHE.


ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.


ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `(BC)/(BR) = 5/4` then construct ∆ABC and ΔPBR.


If the point P(6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio.

Solution:

Point P divides segment AB in the ratio m : n.

A(8, 9) = (x1, y1), B(1, 2) = (x2, y2) and P(6, 7) = (x, y)

Using Section formula of internal division,

∴ `7 = (m(square) - n(9))/(m + n)`

∴ 7m + 7n = `square` + 9n

∴ 7m – `square` = 9n – `square`

∴ `square` = 2n

∴ `m/n = square`


To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is ______.


To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, .... are located at equal distances on the ray AX and the point B is joined to ______.


To construct a triangle similar to a given ΔABC with its sides `3/7` of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, ... on BX at equal distances and next step is to join ______.


To construct a triangle similar to a given ΔABC with its sides `8/5` of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. Then minimum number of points to be located at equal distances on ray BX is ______.


For ∆ABC in which BC = 7.5cm, ∠B =45° and AB - AC = 4, select the correct figure.


The ratio of corresponding sides for the pair of triangles whose construction is given as follows: Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60°.A ray BX is drawn from B making an acute angle with AB.5 points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.

B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A’.

Another line is drawn through A’ parallel to AC, intersecting the extended line BC at C’. Find the ratio of the corresponding sides of ΔABC and ΔA′BC′.


If I ask you to construct ΔPQR ~ ΔABC exactly (when we say exactly, we mean the exact relative positions of the triangles) as given in the figure, (Assuming I give you the dimensions of ΔABC and the Scale Factor for ΔPQR) what additional information would you ask for?


If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?


The image of construction of A’C’B a similar triangle of ΔACB is given below. Then choose the correct option.


The basic principle used in dividing a line segment is ______.


To divide a line segment, the ratio of division must be ______.


Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.


Draw a line segment of length 7.5 cm and divide it in the ratio 1:3.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×