k 2 geometry

Equation of the line passing through the intersection of two lines - Let the lines be Let P (h,k) be the point of intersection of L 1 = 0 and L 2 = 0. Now consider the following equations, (v) (vi) This equation is a first degree in x and y and hence this represents a ..

Locus of points equidistant from two given points - Mark two points M and N, 6 cm apart. Locate points P 1 and P 2 on either side of AB such that P 1 M=P 1 N=3.5 cm Locate points Q 1 and Q 2 such that Q 1 M = Q 2 M = 4.5 cm Observe the pattern of ge..

Question: Find the equation of the line perpendicular to the line 8x + 5y = 7 and passing through (1, 2). Answer: ( Product of slopes of two perpendicular lines = -1) ..

are parallel to the sides of The point X is called the centre of enlargement. Let us consider various cases for different values of the enlargement factor. Enlargement factor greater than one. when K > 1 Let K = 2 Take O as the centre of enlargement, two p..

Summary - Enlargement or Dilatation If D PQR is the image of D ABC (Pre image) and K is the enlargement factor, If K = 1 the triangles are congruent. The ratio of their areas is K 2 (SAS similarity) If a pair of corresponding angles are equal and the sides in..

Similarity - Study the following figures. They have the same shape though their sizes are different. One figure is the enlargement of the other figure. These figures are said to be similar to each other. In our study, we mostly deal with similarity of triangles. Two triangles are similar ..

Question: The line segment joining A(2,3) and B(6,-5) is intersected by the x-axis at point K. Write down the ordinate of K. Hence find the ratio in which K divides AB. [3 Mark] Answer: The point K is on the x-axis. Therefore, the o..

Question: In what ratio does the point divide the line segment joining the points (3,-5) and (-7,9)? [2 Mark] Answer: Let the point divide the line segment joining A(3,-5) and B (-7,9) in the ratio k:1. ..

Let the equation of the line AB be ax + by + c = 0 (i) Let P(x 1 , y 1 ) be the given point. Draw PN perpendicular to AB. Let the equation of PN be bx - ay + k = 0 (ii) (ii) - (iii) = b(x - x 1 ) - a(y - y 1 ) = 0 (iv) Let N be (x 2 ,y 2 ). ..

(Two-point form) Here, we assume that x 1 x 2 ; in case x 1 = x 2 , then the line is vertical and its equation is x = x 1 (or x 2 ) The equation of the straight line passing through (x1, y1) and making angle q with the positive direction of x-axis is given by..