MATHEMATICS 10Second Quarter(Week 7 – Day 1 to 2)MOST ESSENTIAL LEARNING COMPETENCYApplies the distance formula to prove some geometric propertiesOBJECTIVEDerive the distance formulaWHAT I KNOWMultiple Choice: Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.1. Which of the following represents the distance dbetween two points?a. d = √(x2+x1)2+(y2+y1)2b. d = √(x2+x1)2−(y2+y1)2c. d = √(x2−x1)2+(y2−y1)2d. d = √(x2−x1)2−(y2−y1)22. What is the distance between point M (-3, 1) and N (7, -3)?3. If the coordinates of P and Q are (-2, 5) and (8,5) respectively, which of the following would give the distance between two points?4. What is the distance of A( 6,8 ) and B ( 12,10) ?5. Which among the points have a distance of 14.56 units?a. ( -3, 2) (11, 6) b. (-5,-1) ( 8,6) c. (-7,11) (-9,3) d. (0,8) (-10,0)WHAT’S INHave you ever wondered how engineers find the distance of two places that, even if it’s very far from each other?What is a distance?Distanceis a numerical measurement of how far apart objects or points are. Mathematical Distanceis defined as the amount of space between two points. This distance can be calculated using the distance formula.WHAT’S NEW The graph of the given coordinates of two points with the same x-coordinate is a vertical lineand the graph of the given coordinates of two points with the same y-coordinate is a horizontal line. In this case you can simply use the absolute valueof these different x- or y- coordinate.AB = |5−2|= 3 units CD = |2−6|= |−4|= 4 unitsHow about if the given coordinates of two points will form a slanting line? How will you find its distance with each other? Sometimes it is hard to count the units on a coordinate plane, that’s why we have the Distance Formula.