Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Coordinate Geometry

Short Answer Type

191. Name the type of triangle formed, if any, by the following points and give reason for your answer :

left parenthesis straight a comma space straight a right parenthesis comma space left parenthesis negative straight a comma space minus straight a right parenthesis comma space left parenthesis negative straight a square root of 3 comma space straight a square root of 3 right parenthesis

80 Views

Long Answer Type

192. Name the type of triangle formed, if any, by the following points and give reason for your answer:

left parenthesis 1 comma space minus 1 right parenthesis comma space space open parentheses fraction numerator negative 1 over denominator 2 end fraction comma space 1 half close parentheses space left parenthesis 1 comma space 2 right parenthesis

92 Views

Short Answer Type

193. Name the type of triangle formed, if any, by the following points and give reason for your answer:

open parentheses negative 2 comma space 0 close parentheses comma space open parentheses negative 4 comma space minus 2 square root of 3 close parentheses comma space left parenthesis negative 6 comma space straight C right parenthesis.

98 Views

194. Determine by distance formula, whether the given points are collinear :
(1, 2), (9, 3) and (17, 4)

162 Views

195. Determine by distance formula, whether the given points are collinear :
(-1, 2), (5, 0) and (2, 1).

124 Views

196. Find a point on jr-axis which is equidistant from (-5, -2) and (3, 2).

85 Views

197. Find the point on x-axis which is equidistant from the points (2, -5) and (-2,

148 Views

198. Find the relation between x and y such that point (x, y) is equidistant from the points (6, -1) and (2, 3).

Let P(x, y), A(6, -1) and B(2, 3) be the given points
It is given that :AP = BP

$rightwards double arrow square root of left parenthesis straight x minus 6 right parenthesis squared plus left curly bracket straight y minus left parenthesis negative 1 right parenthesis right curly bracket squared end root equals square root of left parenthesis straight x minus 2 right parenthesis squared plus left parenthesis straight y minus 3 right parenthesis squared end root rightwards double arrow square root of left parenthesis straight x minus 6 right parenthesis squared plus left parenthesis straight y plus 1 right parenthesis squared end root equals square root of left parenthesis straight x minus 2 right parenthesis squared plus left parenthesis straight y minus 3 right parenthesis squared end root rightwards double arrow square root of straight x squared plus 36 minus 12 straight x plus straight y squared plus 1 plus 2 straight y end root equals square root of straight x squared plus 4 minus 4 straight x plus straight y squared plus 9 minus 6 straight y end root rightwards double arrow square root of straight x squared plus straight y squared minus 12 straight x plus 2 straight y plus 36 plus 1 end root equals square root of straight x squared plus straight y squared minus 4 straight x minus 6 straight y plus 9 plus 4 end root$

Squaring both side, we get
x² + y² - 12x + 2y + 36 + 1
= x² + y² -4x - 6y + 9 + 4
⇒ -8x + 8y + 24 = 0
⇒ -8(x - y - 3) = 0
⇒ x - y - 3 = 0 ⇒ x - y = 3.

122 Views

199. Show that the points A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle.

485 Views

Long Answer Type

200. Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6, 2) arc the vertices of a square.

162 Views