A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.

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

A gardener buys two kinds of fertilizer. Fertilizer A contains  filler materials by weight and Fertilizer B contains  filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y  is the number of pounds of Fertilizer B?

State and prove the Midsegment Theorem.

Find the midpoint and length of each side using the placement
below. What is the advantage of using 2h instead of h for the leg lengths?

A sum of Rs. 4,000 is lent for 5 years at the rate of 15% per annum. Find the simple interest.?

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?