Points A (-5, 10), B (8, 10) and C (25, 10) lie on a straight line.The following are a few statements concerning these points on the line.I. The line is vertical.II. The line is horizontal.III. The length of AB is 12 units shorter than that of AC.IV. The length of AB is 17 units shorter than that of AC.Which of the following statement(s) is/are true?
Question
Points A (-5, 10), B (8, 10) and C (25, 10) lie on a straight line.The following are a few statements concerning these points on the line.I. The line is vertical.II. The line is horizontal.III. The length of AB is 12 units shorter than that of AC.IV. The length of AB is 17 units shorter than that of AC.Which of the following statement(s) is/are true?
Solution 1
The statements that are true are II and IV.
Here's why:
I. The line is not vertical. In a vertical line, the x-coordinate remains the same while the y-coordinate changes. Here, the y-coordinate is the same (10) while the x-coordinate changes (-5, 8, 25), so the line is not vertical.
II. The line is horizontal. In a horizontal line, the y-coordinate remains the same while the x-coordinate changes. Here, the y-coordinate is the same (10) while the x-coordinate changes (-5, 8, 25), so the line is horizontal.
III. The length of AB is not 12 units shorter than that of AC. The length of a line segment is the difference in the x-coordinates (since this is a horizontal line). So, AB = 8 - (-5) = 13 units and AC = 25 - (-5) = 30 units. The difference is 30 - 13 = 17 units, not 12.
IV. The length of AB is 17 units shorter than that of AC. As calculated above, AB = 13 units and AC = 30 units. The difference is 30 - 13 = 17 units, so this statement is true.
Solution 2
The correct statements are:
II. The line is horizontal. This is true because all three points have the same y-coordinate, which means they lie on the same horizontal line.
III. The length of AB is 12 units shorter than that of AC. This is true because the distance between points A and B (AB) is the absolute difference of their x-coordinates, which is 13 units (8 - (-5)). Similarly, the distance between points A and C (AC) is the absolute difference of their x-coordinates, which is 30 units (25 - (-5)). Therefore, AB is indeed 17 units shorter than AC.
IV. The length of AB is 17 units shorter than that of AC. This statement is false. As calculated above, AB is 12 units shorter than AC, not 17.
I. The line is vertical. This statement is false. As mentioned above, the line is horizontal, not vertical.
Similar Questions
Study the following information carefully and answer the question given below:(i) A, B, C, D, E, F, G and H are eight students, each having a different height.(ii) D is shorter than A but taller than G.(iii) E is taller than H but shorter than C.(iv) B is shorter than D but taller than F.(v) C is shorter than G.(vi) G is not as tall as F.Which of the following is definitely false?
P (5, -1) and Q (5, 10) lie on a straight line.The following are a few statements concerning these points on the line. I. The gradient of the straight line is undefined.II. The gradient of the straight line is zero.III. (-5, 8) lies on the straight line. Which of the following statement(s) is/are true?
Line m passes through the points (3, 7) and (6, 12) while line n passes through the points (-5, 1) and (-2, 6).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are parallel.B.Lines m and n have opposite reciprocal slopes so they are perpendicular.C.Lines m and n have the same slope so they are perpendicular.D.Lines m and n have opposite reciprocal slopes so they are parallel.
If two line segments are congruent, which of the following must be true?A.They have equal lengths.B.They share an endpoint.C.They are equal.D.They form a right angle.
Show that each statement is false by providing a counterexample.(a)If the length of AC is 46 and point B lies on AC, then =AB34 and =BC12.=Counterexample:AB=, BC(b)If the perimeter of a rectangle is 12, then the length is 3 and the width is 3.=Counterexample:length=, width(c)If ∠1 and ∠2 are complementary angles, then one of them must have a measure less than 45°.=Counterexample:m∠1=, °m∠2°(d)If the measures of ∠R, ∠S, and ∠T sum to 180°, then one of the angles must be obtuse.=Counterexample:m∠R=, °m∠S=, °m∠T°
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.