Question

.1. If (1,x) is at a distance of √10 units from (0,0) , find the value of x.
2. Find the value of k such that AB=BC, where A= (6,-1), B= (1,3), C= (k,8) respectively.
3. Find the point on the y- axis equidistant from (7,6) and (-3,4).
4. Show that (-2,2), (8,-2) and (-4,-3) are the vertices of a right triangle.
5. Show that A= (3,4) , B=(4,2), C=(5,-4), D=(4,-10) are the vertices of a rhombus.
6.Show that (-3,-4) , (12,5),(14,12) and (-1,3) are the vertices of a parallelogram.
7. Show that (-1,-8),(4,-6),(2,-1),(-3,-3) are the vertices of a square.
8. If A= (-3,-2), B=(3,2) , C = (2√3, 3√3), show that triangle ABC is equilateral.
9.If a circle passes through (1,2) with its center at origin, find its radius.
10. Find the ratio in which  the line segment joining the points  (-2,3) and (5,-4) is divided by i) x-axis ii)y-axis
11. the centroid of a triangle is (2,7). if two of its vertices are (4,8) and (-2,6). find the third vertex.
12.Find the fourth vertex of the parallelogram ABCD , if A=(-2,-1) , B= (1,0) and C=(4,3)
13.The slope of the line perpendicular to the line 2x-3y+6=0 is 
14. the line passing through the points (2,6) and (-2,6) is 
     a) parallel to x-axis.    b) parallel to y-axis

Answer 1

Hi this is answered by Prmkulk1978 :  https://brainly.in/question/2479570

Answer:

The third vertex of triangle is :(3,1)

Step-by-step explanation:

Let the third vertex be (x,y)  and other two vertices are (-3,1) and (0,-2)

Coordinates of  centroid  of triangle  =(0,0)

∴ [-3+0+x/3 , 1-2+y/3] = (0,0)

-3+x/3 = 0

x-3=0

x=3

and 1-2+y/3 =0

y-1/3=0

y-1=0

y=1

∴ x=3 and y=1