The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is
(A) (– 4, – 6) (B) (2, 6) (C) (– 4, 2) (D) (4, 2)
If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is
(A) –2 (B) 2 (C) –1 (D) 1
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.
Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB DC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that PO = QO.
In Fig. PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS.
In ∆ PQR, PD ⊥ QR such that D lies on QR . If PQ = a, PR = b, QD = c and DR = d, prove that (a + b) (a – b) = (c + d) (c – d).
In Fig. PQR is a right triangle right angled at Q and QS ⊥ PR . If PQ = 6 cm and PS = 4 cm, find QS, RS and QR.
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