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11 May 2021, 02:30
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D
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Difficulty:
35%
(medium)
Question Stats:
74% (02:08) correct
26%
(01:14)
wrong
based on 53
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The equation of line m is y=x/2+1. What is the distance from the x-intercept of m to the intersection of x=4 and m?
A. √(13)
B. 5
C. 6
D. 3√5
E. 7
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16 May 2021, 10:45
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To answer this question, we will define:
point A as the point of line m passing x intercept; and
point B as the point of line m when x=4
The question is simply asking the distance between point A and point B
Point A is defined as (X', 0)
To get the X', we will plug in y=0 (x intercept) to the line m equation
y = x/2 + 1
(0) = x/2 + 1
x/2 = -1
x = -2
Therefore X' is -2 and point A is (-2, 0)
Point B is defined as (4, Y')
To get the X', we will plug in x=4 to the line m equation
y = x/2 + 1
y = (4)/2 + 1
y = 2 + 1
y = 3
Therefore Y' is 3 and point B is (4, 3)
From here, you can see that there is a triangle for point A, point B, and point (4, 0)
We will leverage this to calculate the distance of point A to point B
the triangle will have the length of 4 - X' = 4 - (-2) = 6; and
the triangle will have the height of Y' - 0 = (3) - 0 = 3
Using the Pythagorean theorem, we will get that the distance between A and B are as follows:
= \sqrt{(length of triangle)^2 + (height of triangle)^2}
= \sqrt{(6)^2 + (3)^2}
= \sqrt{36 + 9}
= \sqrt{45}
= \sqrt{9 * 5}
= \sqrt{9} * \sqrt{5}
= 3\sqrt{5}
Therefore, the distance between A and B is 3\sqrt{5}
answer D
point A as the point of line m passing x intercept; and
point B as the point of line m when x=4
The question is simply asking the distance between point A and point B
Point A is defined as (X', 0)
To get the X', we will plug in y=0 (x intercept) to the line m equation
y = x/2 + 1
(0) = x/2 + 1
x/2 = -1
x = -2
Therefore X' is -2 and point A is (-2, 0)
Point B is defined as (4, Y')
To get the X', we will plug in x=4 to the line m equation
y = x/2 + 1
y = (4)/2 + 1
y = 2 + 1
y = 3
Therefore Y' is 3 and point B is (4, 3)
From here, you can see that there is a triangle for point A, point B, and point (4, 0)
We will leverage this to calculate the distance of point A to point B
the triangle will have the length of 4 - X' = 4 - (-2) = 6; and
the triangle will have the height of Y' - 0 = (3) - 0 = 3
Using the Pythagorean theorem, we will get that the distance between A and B are as follows:
= \sqrt{(length of triangle)^2 + (height of triangle)^2}
= \sqrt{(6)^2 + (3)^2}
= \sqrt{36 + 9}
= \sqrt{45}
= \sqrt{9 * 5}
= \sqrt{9} * \sqrt{5}
= 3\sqrt{5}
Therefore, the distance between A and B is 3\sqrt{5}
answer D
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24 May 2021, 21:36
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Given
To find
Approach and Working out:
x -intercept of line m
Distance between (4,3) and (-2, 0)
Hence, option D is the correct answer.
Correct Answer: Option D
- • The equation of line m is y=\(\frac{x}{2}\)+1.
To find
- • Distance from the x-intercept of m to the intersection of x=4 and m
Approach and Working out:
x -intercept of line m
- • To get the x-intercept, put y=0
- o 0 = \(\frac{x}{2}\) +1
o \(\frac{x}{2}\) = -1
o x = -2
- • Intersection point of x=4 and y =\(\frac{x}{2}\) +1
- o y =\(\frac{4}{2}\) +1 = 2+1 =3
o Coordinates at the point of intersection =(4,3)
Distance between (4,3) and (-2, 0)
- • Distance=\(\sqrt{(4+2)^2 +3^2)}\)= \(\sqrt{(36+9)}\) = \(\sqrt{45}\)
- o Distance = 3\(\sqrt{5}\)
Hence, option D is the correct answer.
Correct Answer: Option D
