`X` and `Y` are two points on the sides `PQ` and `PR` respectively of the `DeltaPQR`.
`(a)` If `PX=2` units, `XQ=3.5` units,`YR=7` units and `PY=4.25` units, then find whether`XY` and `QR` are parallel or not.
`(b)` If `PQ=8` units, `YR=12` units, `PY=4`units and the length of `PY` is `2` units less than that of `XQ`, then find whether `XY` and `QR` are parallel or not.

In a cyclic quadrilateral PQRS, PQ= 2 units, QR= 5 units, RS=3 units and /_P Q R=60^0, then what is the measure of SP?

In trapezium PQRS , PQ||SR . If PQ=4 units , SR=6 units . If the diagonals of the trapezium intersect each other at the points C , then find the ratio CQ:CS .

A line parallel to the side BC of DeltaABC intersects the sides AB and AC at the points P and Q respectively. (a) If PB=AQ , AP=9 units, QC=4 units, then calculate the length of PB . (b) The length of PB is twice of AP and the length of QC is 3 units more than the length of AQ , then calculate the length of AC . (c ) If AP=QC , the length of AB is 12 units and the length of AQ is 2 units , then calculate the length of CQ .

The area of a rectangle is 8x^2 sq units. If its length is 4x units, find its breadth.

The points P and Q are on the first and third quadrant respectively and the distances of them from the x-axis and y-axis are 6 units and 4 units respectively. Find the coordinates of mid-point bar(PQ) .

In triangleXYZ , angleY = 90^@ . If XY = 2sqrt3 unit and XZ-YZ = 2 units, find the value of secX + tan X

In trianglePQR , a line parallel to QR meets PQ and PR at X and Y. If PX = 4.8cm., PY = 6.4cm. And YR = 9.6cm. Then the length of PQ is

The area of a rectangle is 8x^2sq.units. . If the length ios 4x units. Let's find its breadth.

The points A and B lie on the second and fourth quadrant respectively and the distances of them from the x-axis and y-axis are 8 units and 6 units respectively. Find the coordinates of mid-point of AB.

Distance between (x,-7) and the point (3,-3) is 5 unit . Find the value of x.