Place a rectangle in a coordinate plane in a way that is
convenient for finding side lengths. Assign coordinates to each vertex.
 

MN is the midsegment of △ ABC.
Find MN.
Also, find AC if CN = 35 cm

In △ ABC, AM ≅ BM
BQ ≅ QC
Prove that MQ ∥ AC.

Write a coordinate proof.
Any right isosceles triangle can be subdivided into a pair of congruent right isosceles triangles.(Hint: Draw the segment from the right angle to the midpoint of the hypotenuse.)

NQ, MN and MQ are the midsegments of △ ABC. Find BM.

MN is the midsegment of △ ABC.
Find MN if BC = 35 m.

MN is the midsegment of △ ABC.
Find BC if MN = 17 cm.

In the figure above, RT = TU. What is the value of x?

For the graph below , write an inequality and explain the reasoning :

Note:
We do not use < or > for infinity in inequalities, since the variable extends to infinite and has no real fixed value.

In what time will Rs 10000 earn an interest of Rs. 12600 at 18% per annum simple interest?

The formula below is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time.

Which of the following correctly gives P in terms of E, O, and M?

A square has vertices (0, 0), (3, 0), and (0, 3). Find the fourth
Vertex.

Let a, b and c be real numbers, c≠0, Show that each of the following statements is true :
1. If a>b and c<0 , then ca< cb
2. If a>b and c<0 , then .

Note:
Whenever we multiply or divide an inequality by a negative number, the direction of the inequality symbol changes.

The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m?

3x + x + x + x - 3 – 2 = 7+ x + x
In the equation above, what is the value of x?

A certain sum at simple interest amounts to Rs. 3,900 in 3 years and Rs. 4,500 in 5 years. Find the sum and rate of interest per annum.