Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively. (a) Prove that E is the midpoint of PQ. (b) Show that PQ=1/[1/2(1/a + 1/b)] . PQ is known as the harmonic mean of a & b.

Q: P = (9,6,1) R = (9,8,5) Find the point such that R is the midpoint of PQ.

A: given R is midpoint of PQ  if two points is (x1,y1,z1) and (x2,y2,z2)then coordinates of midpoint is…

Q: BC cuts the x-axis at D. E is a point on AC such that BA // DE. Given points A(-4,8), B(5,2),…

A:

Q: Evaluate fr (y-x-3x²i)dz where C is the straight line from z = = 0 to z = 1 + i. 2+i

A:

Q: ) Determine the Cartesian Equation perpendicular to the line L1: 4t – 2y = 8, -3t = 6 – 2x with a…

A: Write L1 in Cartesian form. Then find its slope or gradient then use it to find the slope of the…

Q: Si -x- 2y - 3x + y R - x - 2y = 0, - x - 2y = 9, Find -dA, where R is the parallelogram enclosed by…

A:

Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: [i] Let ABCD be a parallelogram where A is (2,−1,−3), B is (1,0,−2) and C is (2,3,1). (a) Find the…

A:

Q: M(1.5) J4,5) Which statement proves that quadrilateral JKLM is a kite? ZM is a right angle and MK…

A: A quadrilateral is said to be a kite if it's four sides can be partitioned into two pairs of sides…

Q: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

A:

Q: 5x - 7y + 5z = -52 and 6x - 2y + 2z = -4.

A: