Question

(b) Sketch the plane representing -2x, = -8
(c) Given the points (-4,8) and (6, -12)
(1) Determine the midpoint of the line segment connecting the points.
(ii) Determine the distance separating the two points
​

Answer 1

Answer:

(b) -2x=-8

x=4

so graph is parallel to y-axis.

(c)let the given points are

A(-4,8) and B(6,-12)

for mid point we have to use mid point formula

mid point=(($x_{1}$+$x_{2}$)÷2,  ($y_{1\\}$+$y_{2}$)÷2)

(ii) for this we have to use distance formula which is as following

d=$\sqrt{(x_{2} -x_{1} )^2-(y_{2} -y_{1})^2 }$

Step-by-step explanation:

Answer 2

(a) Sketch the plane representing -2x1 = -8

Answer :-

→ -2x1 = -8

→ x1 = (-8)/(-2) = 4

now, draw a line passes from positive 4 on x - axis and which is parallel to y - axis .

(b) Given the points (-4,8) and (6, -12)

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

(ii) Determine the distance separating the two points .

Answer :-

we know that, Mid points of points (a,b) and (c,d) is ,

• (a + c)/2 and (b + d)/2

so,

→ The midpoint of the line segment connecting (-4,8) and (6,-12) = (-4 + 6)/2 and (8 - 12)/2 = (2/2) and (-4/2) = (1, -2) .

now, we know that, distance between two points (a,b) and (c,d) is,

• √[(a - c)² + (b - d)²]

so,

→ Distance between (-4,8) and (6, -12) = √[(-4 - 6)² + {8 - (-12)}²] = √[(-10)² + (20)²] = √(100 + 400) = √500 = 10√5 units .

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