Question

Given the points (-4,8) and (6,-12):
(i) Determine the midpoint of the line segment connecting the points.
(ii) Determine the distance separating the two points.​

Answer 1

Step-by-step explanation:

Given :-

The points (-4,8) and (6,-12)

To find :-

(i) Determine the midpoint of the line segment connecting the points.

(ii) Determine the distance separating the two points.

Solution :-

Given points are (-4,8) and (6,-12)

Let (x1, y1) = (-4,8) => x1 = -4 and y1 = 8

Let (x2, y2) = (6,-12) => x2 = 6 and y2 = -12

i) The coordinates of the mid point of the line segment joining the points (x1, y1) and (x2, y2) is ( { x1+x2}/2 , {y1+y2}/2 )

On Substituting these values in the above formula then

=> ( {-4+6}/2 , {8+(-12)}/2 )

=> ( 2/2 , {8-12}/2 )

=> (2/2 , -4/2)

=> (1 , -2)

ii) The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

=> √[(6-(-4))²+(-12-8)²]

=> √[(6+4)²+(-20)²]

=>√(10²+(-20)²)

=> √(100+400)

=>√500 units

=> √(5×100) units

=> 10√5 units

Answer:-

i) The coordinates of the mid point of the linesegment joining the given points is (1,-2)

ii) The distance between two given points is

√500 units (or) 10√5 units

Used formulae:-

Mid Point formula :-

• The Coordinates of the mid point of the line segment joining the points (x1, y1) and (x2, y2) is

({x1+x2}/2 , {y1+y2}/2 )

Distance formula:-

• The distance between two points

(x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units