Translate the sentence into an equation.
1 answer:
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Answer:
The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis
Step-by-step explanation:
*<em> Lets explain how to solve the problem</em>
- Any point will be equidistant from the x-axis and the y-axis must have
equal coordinates
- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis
because the distance from the x-axis to the point is 4 (y-coordinate)
and the distance from the y-axis and the point is 4 (x-coordinate)
- If (x , y) is the mid-point of a segment its endpoints are
and
, then
and
* <em>Lets solve the problem</em>
∵ Point A has coordinates (p , q)
∵ Point B has coordinates (p + 2q , q + 2p)
- The mid-point of AB is (x , y)
∵
∴
- Take 2 as a common factor from the terms of the numerator
∴
- Divide up and down by 2
∴ x = p + q
∵
∴
- Take 2 as a common factor from the terms of the numerator
∴
- Divide up and down by 2
∴ y = q + p
∴ <em>The mid point of AB is (p + q , q + p)</em>
- p + q is the same with q + p
∵ The x-coordinate of the mid point of AB is p + q
∵ The y-coordinate of the mid point of AB is q + p
∵ p + q = q + p
∴ The coordinates of the mid-point of AB are equal
- According the explanation above
∴ The mid-point (p + q , q + p) of AB is the same distance from the
x-axis and the y-axis
Answer:
A
Step-by-step explanation:
Calculate the slope of the given points with the point (- 2, 5 )
If the slope is - then the point is on the line
Calculate slope m using the slope formula
m =
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 1)
m = =
= -
← point (6, - 1) is on the line
Repeat with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (2, 8)
m = =
← point (2, 8) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (- 5, 1)
m = =
=
← point (- 5, 1) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (1, 1)
m = = -
← point (1, 1) is not on the line
Thus the point on the line is (6, - 1 ) → A