Geometry Answers

In the coordinate plane the point x (-4,4) is translated to the point x (0,-1). Under the same translation the points Y (-2,0) and Z (-1,6) are translated to Y and Z, respectively. What are the coordinates of Y and Z?

QC is a median of triangle PQR. The incircle of triangle PQR intersects this median at points A and B, and at that A lies between Q and B, and QA : AB : BC=1:2:1. Find the ratio of the largest side of triangle PQR to its smallest side.

ABCD is a right trapezoid (\angle A = 90°), its diagonals intersect at point G. The circle with diameter AB is tangent to lateral side CD of the trapezoid at point H. Find the length of base BC provided that GH = 5, AD = 7.

Jonny is writing a program for a video game. For one part of the game he uses the rule given bellow to move objects on the screen. Give the output that the rule gives for the inputs. (X,y)

given the points below, find xy. round to the nearest hundredth. x(-1,2) and y(4,0)

M<PXQ=(8x-3)°,m<PXS=(10x+30)°,find the value of ‘x’ and m<QXS

Polygons

Jonny is writing a program for a video game. For one part of the game he uses the rule given below to move objects on the screen.

Showing all your work, give the output that the rule gives for the inputs.

(x, y)→(x−7.5, y+6.8)

{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>,</mo><mo>&#xA0;</mo><mi>y</mi><mo>)</mo><mo>&#x2192;</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo>&#xA0;</mo><mi>y</mi><mo>+</mo><mn>6</mn><mo>.</mo><mn>8</mn><mo>)</mo></math>"}

First input: (4.4, 2.5)

Second input: (9.7, -2.9)

Q2. Find the distance of 𝑃(−3,2) from the line with equation 5𝑥 + 12𝑦 + 11 = 0.