7
a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4
b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units
c. The midpoint of the R(3, 5) and H(-1,2) is (2, 4)
8.
a. The transformation rule is (x,y) → (x + 1, y - 1)
b.
- The x-coordinate is shifted 1 unit to the left and
- The y - coordinate is shifted 1 unit downwards.
c. The image of B' the pre-image of B(5, 6) is (6, 5)
<h3 /><h3>7 a. How to find the slope of the line?</h3>
The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)
Given that
- (x₁, y₁) = (3, 5) and
- (x₂,y₂) = (-1, 2)
So, m = (y₂ - y₁)/(x₂ - x₁)
m = (2 - 5)/(-1 - 3)
m = -3/-4
m = -3/4
So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4
<h3>b. The distance between the points</h3>
The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]
Given that
- (x₁, y₁) = (3, 5) and
- (x₂,y₂) = (-1, 2)
d = √[(y₂ - y₁)² + (x₂ - x₁)²]
d = √[(2 - 5)² + (-1 - 3)²]
d = √[(-3)² + (-4)²]
d = √[9 + 16]
d = √25
d = 5 units
So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units
<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>
The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Given that
- (x₁, y₁) = (3, 5) and
- (x₂,y₂) = (-1, 2)
So, the midpoint (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]
(x, y) = [(3 + (-1))/2, (5 + 3)/2]
(x, y) = [(3 - 1)/2, (5 + 3)/2]
(x, y) = [4/2, 8/2]
(x, y) = (2, 4)
So, the midpoint of the R(3, 5) and H(-1,2) is (2, 4)
<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>
Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).
Let pont A be (x,y).
So, point B = (x + 1, y - 1)
So, the transformation rule is (x,y) → (x + 1, y - 1)
<h3>b. Describe the transformation</h3>
Since the transformation rule is (x,y) → (x + 1, y - 1), we see that
- the x-coordinate is shifted 1 unit to the left and
- the y - coordinate is shifted 1 unit downwards.
<h3>c. The image of B' the pre-image of B(5, 6)</h3>
Since the transformation rule is (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is
(x,y) → (x + 1, y - 1)
(5,6) → (5 + 1, 6 - 1)
(5,6) → (6, 5)
So, the image of B' the pre-image of B(5, 6) is (6, 5)
Learn more about slope of a line here:
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x + 4