What equation is graphed in this figure?
1 answer:
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Angles formed by the segment in the triangles ΔWXZ, and ΔXYZ, are equal and the given corresponding sides are proportional.
- The option that best completes the proof showing that ΔWXZ ~ ΔXYZ is; <u>16 over 12 equals 12 over 9</u>
Reasons:
The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;
Segment is perpendicular to segment
∠WZX and ∠XZY are right angles by definition of perpendicular to
∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)
Therefore;
, which gives,
Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and
that the included angles between the two sides, ∠WZX and ∠XZY are
congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-
Side, SAS, similarity postulate.
The option that best completes the proof is therefore;
Learn more about the SAS similarity postulate here:
Answer:
A. y = 2x -9
B. y = -1/2x +1
Step-by-step explanation:
The given line is in slope-intercept form
y = mx + b
where m is the slope. For your given line, the slope is 2.
A. A parallel line will have the same slope. It is convenient to start with a point-slope form of the equation for the line:
y = m(x -h) +k . . . . . for slope m through point (h, k)
You want the equation of the line through (4, -1) with slope 2, so its equation is ...
y = 2(x -4) -1
Simplifying to slope-intercept form, this becomes ...
y = 2x -8 -1
y = 2x -9
___
B. A perpendicular line will have a slope that is the opposite of the reciprocal of the slope of the given line. That slope is ...
m = -1/2
As above, the point-slope form of the perpendicular line is ...
y = -1/2(x -4) -1
y = -1/2x +1 . . . . . after simplification
