GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Line k lies in the xy-plane. The x-intercept of line k is a
[#permalink]
14 Dec 2015, 07:15
14 Dec 2015, 07:15
3
Expert Reply
9
Bookmarks
00:00
Question Stats:
62% (01:38) correct
37% (01:36) wrong based on 146 sessions
Hide Show timer Statistics
Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes through the midpoint of the line segment whose endpoints are and (2, 9), and (2, 0). What is the slope of line k ?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{3}{4}\)
Practice Questions
Question: 12
Page: 153
Difficulty: medium
Question: 12
Page: 153
Difficulty: medium
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Line k lies in the xy-plane. The x-intercept of line k is a
[#permalink]
05 Jul 2020, 05:02
05 Jul 2020, 05:02
5
Carcass wrote:
Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes through the midpoint of the line segment whose endpoints are and (2, 9), and (2, 0). What is the slope of line k ?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{3}{4}\)
GIVEN: The x-intercept of line k is -4
The y-coordinate is always 0 at any x-intercept.
So, we now know that line K passes through the point (-4, 0)
GIVEN: line k passes through the midpoint of the line segment whose endpoints are and (2, 9), and (2, 0)
The MIDPOINT of a line segment with endpoints (2, 9), and (2, 0) is (2, 4.5)
So, we now know that line K passes through the point (2, 4.5)
What is the slope of line k?
Slope = rise/run
= (4.5 - 0)/(2 - (-4))
= 4.5/6
= 9/12
= 3/4
Answer: 3/4
Cheers,
Brent
General Discussion
Re: Line k lies in the xy-plane. The x-intercept of line k is a
[#permalink]
14 Dec 2015, 07:41
14 Dec 2015, 07:41
3
Expert Reply
Solution
The coordinates of the first point are since the x-coordinate is and (−4, 0), −4 the y-coordinate of every point on the x-axis is 0. For the second point, the mid-point of the line segment is halfway between the endpoints and (2, 9) (2, 0). Thus, the midpoint has x-coordinate 2 and y-coordinate
\(\frac{9}{2}\) the number halfway between 9 and 0. Based on the coordinates (−4, 0) and \((2, \frac{9}{2})\), the slope of line k is
\(\frac{9}{2}- 0 / 2 - (- 4 )\)
\(=\frac{9}{2}/6\)\(=\frac{3}{4}\)
The coordinates of the first point are since the x-coordinate is and (−4, 0), −4 the y-coordinate of every point on the x-axis is 0. For the second point, the mid-point of the line segment is halfway between the endpoints and (2, 9) (2, 0). Thus, the midpoint has x-coordinate 2 and y-coordinate
\(\frac{9}{2}\) the number halfway between 9 and 0. Based on the coordinates (−4, 0) and \((2, \frac{9}{2})\), the slope of line k is
\(\frac{9}{2}- 0 / 2 - (- 4 )\)
\(=\frac{9}{2}/6\)\(=\frac{3}{4}\)
