5)the midpoint of the sides of a triangle are (3,4),(4,1),(2,0).find the coordinates of the vertices of the triangle.
 
6)for what value of p are the points (2,1),(p,-1),(-1,3) are collinear?
 
7)if the vertices of a triangle are (1,k),(4,-3),(-9,7) and its area is 15 sq units ,find the value of k.
 
8)for what value of p,are the points (-3,9),(2,p) and (4,-5) are collinear?
 
9)find the ratio in which the points (x,2) divides the line segment joining the points (-3,-4) and (3,5). also find the value of x.
 
10)if the pointsA(4,3) and b(x,5) are on the circle with cemtre O(2,3) , find the value of x
 

Asked by snisarulhaq | 2nd Dec, 2017, 02:37: PM

Expert Answer:

begin mathsize 16px style let space left parenthesis straight a comma straight b right parenthesis comma left parenthesis straight c comma straight d right parenthesis space and space left parenthesis straight e comma straight f right parenthesis space be space vertices space of space traingle
let space left parenthesis 3 comma 4 right parenthesis space be space mid space point space of space side space through space left parenthesis straight a comma straight b right parenthesis comma left parenthesis straight c comma straight d right parenthesis
so space
3 equals fraction numerator straight a plus straight c over denominator 2 end fraction comma space space space 6 equals straight a plus straight c....... left parenthesis 1 right parenthesis
4 equals fraction numerator straight b plus straight d over denominator 2 end fraction comma space space space 8 equals straight b plus straight d........ left parenthesis 2 right parenthesis
let space left parenthesis 4 comma 1 right parenthesis space be space mid space point space of space side space through space left parenthesis straight e comma straight f right parenthesis comma left parenthesis straight c comma straight d right parenthesis
so space
4 equals fraction numerator straight e plus straight c over denominator 2 end fraction comma space space space 8 equals straight e plus straight c....... left parenthesis 3 right parenthesis
1 equals fraction numerator straight f plus straight d over denominator 2 end fraction comma space space space 2 equals straight f plus straight d........ left parenthesis 4 right parenthesis
let space left parenthesis 2 comma 0 right parenthesis space be space mid space point space of space side space through space left parenthesis straight a comma straight b right parenthesis comma left parenthesis straight e comma straight f right parenthesis
so space
2 equals fraction numerator straight a plus straight e over denominator 2 end fraction comma space space space 4 equals straight a plus straight e....... left parenthesis 5 right parenthesis
0 equals fraction numerator straight b plus straight f over denominator 2 end fraction comma space space space 0 equals straight b plus straight f........ left parenthesis 6 right parenthesis
add space left parenthesis 1 right parenthesis comma left parenthesis 2 right parenthesis comma left parenthesis 3 right parenthesis comma left parenthesis 4 right parenthesis comma left parenthesis 5 right parenthesis comma left parenthesis 6 right parenthesis
2 straight a plus 2 straight b plus 2 straight c plus 2 straight d plus 2 straight e plus 2 straight f equals 28
straight a plus straight b plus straight c plus straight d plus straight e plus straight f equals 14.... left parenthesis 7 right parenthesis
using space above space equations space find space the space values space of space straight a comma straight b comma straight c comma straight d comma straight e comma straight f

Note space colon space post space questions space one space by space one end style

Answered by Arun | 4th Dec, 2017, 02:44: PM