Use the distance formula to find base and height of the triangle with points (-3, 4), (1, 4), (1, 1) show your work.

The base = 4 units and the height = 3 units

Step-by-step explanation:

* Lets remember the rule of the distance between 2 points

- The two points are (x1 , y1) and (x2 , y2)

∴ The distance = √[(x2 - x1)²+(y2 - y1)²]

* The vertices of the triangles are (-3 , 4) , (1 , 4) , (1 , 1)

- If two points have the same y-coordinate

∴ The line joining the to point is horizontal

∴ Its length = x2 - x1

- Because √[(x2 - x1)²+(y2 - y1)²] and y2 = y1

∴ d = √(x2 - x1)² ⇒ cancel power 2 with the radical sign

∴ d = x2 - x1

* Similar you can find the vertical distance

- If two points have the same x-coordinate

∴ The line joining the to point is vertical

- Its length = y2 - y1

∵ The points (-3 , 4) , (1 , 4) have same y-coordinate

∴ This side of the triangle is horizontal

∴ Its length = 1 - -3 = 4

∵ The points (1 , 4) , (1 , 1) have same x-coordinate

∴ This side of the triangle is vertical line

∴ Its length = 4 - 1 = 3

* The two sides of the triangle are ⊥

∴ One of them is the base of the triangle and the other is the height

* The base = 4 units and the height = 3 units

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b