Question 25 - Show that the points A(-5,6), B(3, 0) and C( 9, 8) are

Question 25 Show that the points A(-5,6), B(3, 0) and C(9, 8) are the vertices of an isosceles triangle. In an isosceles triangle, any 2 of the 3 sides are equal. The three points are A(-5,6), B(3, 0) and C(9, 8) In order to be isosceles, Either AB = AC or AB = BC or BC = AC A (−5, 6) B (3, 0) C (9, 8) We calculate the value of AB, BC & AC by distance formula Calculating AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((𝟑 −(−𝟓))𝟐+(𝟎−𝟔)𝟐) = √((3+5) 2+(−6)2) = √(8 2+62) = √(64+36) = √𝟏𝟎𝟎 = √(10^2 ) = 10 Calculating BC BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 9 −3)2+(8 −0)2) = √(62+82) = √(36+64) = √𝟏𝟎𝟎 = √(10^2 ) = 10 Calculating AC AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 9 −(−5))2+(8−6)2) = √((9+5)^2+22) = √(14^2+22) = √(196+4) = √𝟐𝟎𝟎 Hence, AB = 10, BC = 10, AC = √200 Since AB = BC It satisfies the condition of isosceles triangle Hence, Δ ABC is an isosceles triangle

Question 25 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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