NCERT Class 10 Mathematics

156 MATHEMATICS 7.2 Distance Formula Let us consider the following situation: A town B is located 36 km east and 15 km north of ...

COORDINATE GEOMETRY 157 Therefore, QT = 2 units and PT = RS = 2 units. Now, using the Pythagoras theorem, we have PQ^2 =PT^2 + Q ...

158 MATHEMATICS Let us now find the distance between any two points P(x 1 , y 1 ) and Q(x 2 , y 2 ). Draw PR and QS perpendicula ...

COORDINATE GEOMETRY 159 Also, PQ^2 + PR^2 = QR^2 , by the converse of Pythagoras theorem, we have P = 90°. Therefore, PQR is a ...

160 MATHEMATICS Solution : Using the distance formula, we have AB = (63)^22 ✁(4 1) ✂ 9 ✁ 9 ✂ 18 ✂3 2 BC = (8–6)^22 ✁(6–4) ✂ 4 4✁ ...

COORDINATE GEOMETRY 161 So, the required point is (0, 9). Let us check our solution : AP = (6 – 0)^22 (5 – 9) ✁ 36 16 ✁ 52 BP = ...

162 MATHEMATICS If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR. F ...

COORDINATE GEOMETRY 163 Draw AR, PS and BT perpendicular to the x-axis. Draw AQ and PC parallel to the x-axis. Then, by the AA s ...

164 MATHEMATICS Example 6 : Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, ...

COORDINATE GEOMETRY 165 Therefore, the point (– 4, 6) divides the line segment joining the points A(– 6, 10) and B(3, – 8) in th ...

166 MATHEMATICS Therefore, the coordinates of the points of trisection of the line segment joining A and B are (–1, 0) and (– 4, ...

COORDINATE GEOMETRY 167 EXERCISE 7.2 Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the rat ...

168 MATHEMATICS 7.4 Area of a Triangle In your earlier classes, you have studied how to calculate the area of a triangle when it ...

COORDINATE GEOMETRY 169 Example 11 : Find the area of a triangle whose vertices are (1, –1), (– 4, 6) and (–3, –5). Solution : T ...

170 MATHEMATICS ✁ 1 2( 3) 4( 3 3) 6(3 ) 2 kk✂ ✂ ✄ ✄ ✂ ✄ = 0 i.e., 1 (4) 0 2 ✄ k ☎ Therefore, k = 0 Let us verify our answer. ar ...

COORDINATE GEOMETRY 171 *These exercises are not from the examination point of view. EXERCISE 7.4 (Optional)* Determine the rat ...

172 MATHEMATICS (v) If A(x 1 , y 1 ), B(x 2 , y 2 ) and C(x 3 , y 3 ) are the vertices of ABC, find the coordinates of the cent ...

8 There is perhaps nothing which so occupies the middle position of mathematics as trigonometry. J.F. Herbart (1890) 8.1 Intro ...

174 MATHEMATICS Suppose a hot air balloon is flying in the air. A girl happens to spot the balloon in the sky and runs to her m ...

INTRODUCTION TO TRIGONOMETRY 175 Note that the position of sides change when you consider angle C in place of A (see Fig. 8.5). ...