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Answer:
Step-by-step explanation:
The line that passes through the two points (6, -23) and (11, r) has a slope of 4.
We want to determine the missing value of r.
We can use the slope formula:
Let (6, -23) be (x₁, y₁) and let (11, r) be (x₂, y₂). The final answer should be 4. Therefore:
Simplify and evaluate:
Multiply both sides by 5:
Therefore:
1. The Side Angle Side (SAS) similarity theorem states that:
If two sides of a triangle are proportional to 2 sides of another triangle, and the angles around each of these 2 pairs f sides are equal (congruent), then the triangles are similar.
2. That is, we notice the equivalent ratios:
so
then if m(I)=m(F)=60°, the triangles EFG and HIJ are similar, by SAS similarity theorem.
If two sides of a triangle are proportional to 2 sides of another triangle, and the angles around each of these 2 pairs f sides are equal (congruent), then the triangles are similar.
2. That is, we notice the equivalent ratios:
so
then if m(I)=m(F)=60°, the triangles EFG and HIJ are similar, by SAS similarity theorem.