The figure shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, negative 4, and 0, 0, and 16, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, negative 2 labeled as A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 8, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 8, negative 2 to negative 12, negative 3 labeled as B, one leg is from negative 8, negative 2 to negative 8, negative 3, and the second leg is from negative 12, negative 3 to negative 8, negative 3. Which statement about the slope of the line is true? (5 points)
Answers
To Find :- Which statement about the slope of the line is true ?
A)The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.
B)The slope from point O to point A is 4 times the slope of the line from point A to point B .
C) It is 4 throughout the line .
D) It is fraction 1 over 4 throughout the line.
Answer :-
we have,
- Point on larger shaded ∆ on the line = (0,0) and (-8,-2) .
- Point on smaller shaded ∆ on the line = (-8,-2) and (-12,-3) .
we know that,
- slope of (x1, y1) and (x2,y2) = (y2 - y1)/(x2 - x1) .
so,
→ Slope of larger ∆ = (-2 - 0) / (-8 - 0) = (-2)/(-8) = (1/4) .
→ Slope of smaller ∆ = (-3 + 2) / (-12 + 8) = (-1)/(-4) = (1/4) .
since,
- Slope of larger ∆ = Slope of smaller ∆ = (1/4)
therefore, we can conclude that,
- D) It is fraction 1 over 4 throughout the line.
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